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{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.Probability.Distributions.Gaussian.CharFun","name":"_private.Mathlib.Probability.Distributions.Gaussian.CharFun.0.ProbabilityTheory.gaussian_charFun_congr._simp_1_1","namespace":"_private.Mathlib.Probability.Distributions.Gaussian.CharFun.0.ProbabilityTheory.gaussian_charFun_congr","reducibility":null,"statement_dag_size":402,"type_refs":["AddCommGroup.toAddCommMonoid","Algebra.id","Algebra.to_smulCommClass","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompleteSpace","Complex","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.module","ContinuousLinearMap.toSeminormedAddCommGroup","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Distrib.toMul","DivisionSemiring.toSemiring","Eq","EquivLike.toFunLike","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","InnerProductSpace","InnerProductSpace.toDual","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","LinearIsometryEquiv.symm","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.charFun","MeasureTheory.charFunDual","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toStarRing","Real","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","RingHomInvPair.instStarRingEnd","RingHomIsometric.ids","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","StrongDual","UniformSpace.toTopologicalSpace","instDistribOfSemiring","starRingEnd"],"value_dag_size":411,"value_refs":["AddCommGroup.toAddCommMonoid","Algebra.id","Algebra.to_smulCommClass","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","CompleteSpace","Complex","ContinuousLinearMap.addCommGroup._proof_7","ContinuousLinearMap.module","ContinuousLinearMap.toSeminormedAddCommGroup","DFunLike.coe","DenselyNormedField.toNontriviallyNormedField","DenselyNormedField.toNormedField","Distrib.toMul","DivisionSemiring.toSemiring","Eq.symm","EquivLike.toFunLike","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","InnerProductSpace","InnerProductSpace.toDual","InnerProductSpace.toInner","InnerProductSpace.toNormedSpace","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","LinearIsometryEquiv","LinearIsometryEquiv.instEquivLike","LinearIsometryEquiv.symm","MeasurableSpace","MeasureTheory.Measure","MeasureTheory.charFun","MeasureTheory.charFunDual","MeasureTheory.charFun_toDual_symm_eq_charFunDual","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing","NonUnitalSeminormedRing.toSeminormedAddCommGroup","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedSpace.toModule","PseudoMetricSpace.toUniformSpace","RCLike.innerProductSpace","RCLike.toDenselyNormedField","RCLike.toStarRing","Real","Real.instRCLike","Real.normedField","Real.pseudoMetricSpace","Real.semiring","RingHom.id","RingHomInvPair.instStarRingEnd","RingHomIsometric.ids","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toNonUnitalSeminormedCommRing","SeminormedCommRing.toSeminormedRing","SeminormedRi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ologicalSpace","instDistribOfSemiring","starRingEnd"]}
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