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italRingHomClass","SMulZeroClass.toSMul","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semigroup.toMul","SemigroupWithZero.toSemigroup","SemilatticeSup.toPartialOrder","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","SubfieldClass.toSubringClass","SubringClass.toSubsemiringClass","SubsemiringClass.toCommSemiring","Subtype","Zero.toOfNat0","_private.Mathlib.FieldTheory.RatFunc.Luroth.0.RatFunc.Luroth.b","_private.Mathlib.FieldTheory.RatFunc.Luroth.0.RatFunc.Luroth.c","_private.Mathlib.FieldTheory.RatFunc.Luroth.0.RatFunc.Luroth.Φ","_private.Mathlib.FieldTheory.RatFunc.Luroth.0.RatFunc.Luroth.Φ'","_private.Mathlib.FieldTheory.RatFunc.Luroth.0.RatFunc.Luroth.Φ'_map","_private.Mathlib.FieldTheory.RatFunc.Luroth.0.RatFunc.Luroth.Φ'_ne_zero","_private.Mathlib.FieldTheory.RatFunc.Luroth.0.RatFunc.Luroth.φ","_private.Mathlib.FieldTheory.RatFunc.Luroth.0.RatFunc.Luroth.φ._proof_1","algebraMap_smul","congrArg","id","instDistribOfSemiring","instDistribSMul","instHMul","instHSMul","instIsDomain","instMulZeroClassOfSemiring","instMulZeroOneClassOfSemiring","instNormalizedGCDMonoidOfStrongNormalizedGCDMonoid","inv_mul_cancel₀","map_mul","map_one","mul_assoc","ne_eq","one_mul","propext"]} 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rivativeOn.add","IsCovariantDerivativeOn.leibniz","IsScalarTower.left","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MDifferentiableAt","MDifferentiableAt.inner_bundle","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_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.of_eq","ModelProd","ModelWithCorners","ModelWithCorners.prod","Module.toDistribMulAction","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.instAdd","Pi.smul'","Prod","Prod.normedAddCommGroup","Prod.normedSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","RCLike.toStarRing","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCommSemiring","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toSemiring","RingHom","RingHom.id","RingHom.instFunLike","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TangentSpace","TensorialAt.mk","TopologicalSpace","True","True.intro","UniformSpace.toTopologicalSpace","VectorBundle","WithTop","WithTop.one","Zero.toOfNat0","_private.Mathlib.Geometry.Manifold.VectorBundle.CovariantDerivative.Metric.0.CovariantDerivative.derivMetricTensorAux","_private.Mathlib.Geometry.Manifold.VectorBundle.CovariantDerivative.Metric.0.CovariantDerivative.derivMetricTensorAux_apply","_private.Mathlib.Geometry.Manifold.VectorBundle.CovariantDerivative.Metric.0.CovariantDerivative.tensorial_derivMetricTensorAux₁._abel_1_1","add_apply","chartedSpaceSelf","congr","congrArg","congrFun","congrFun'","conj_trivial","funext","id","inferInstance","inner_add_left","inner_smul_left","instAddCommGroupTangentSpace","instAddMonoidWithOneENat","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instModuleTangentSpace","instMulZeroClassOfSemiring","instSMulOfMul","instTopologicalSpaceModelProd","instTopologicalSpaceTangentSpace","instTrivialStarReal","modelWithCornersSelf","mvfderiv","mvfderiv_fun_add","mvfderiv_fun_mul","rfl","smulCommClass_self","smul_apply","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rivativeOn.add","IsCovariantDerivativeOn.leibniz","IsScalarTower.left","IsSemitopologicalRing.toIsSemitopologicalSemiring","IsSemitopologicalSemiring.toContinuousAdd","IsSemitopologicalSemiring.toSeparatelyContinuousMul","IsTopologicalAddGroup.toContinuousAdd","IsTopologicalDivisionRing.toIsTopologicalRing","IsTopologicalRing.toIsSemitopologicalRing","MDifferentiableAt","MDifferentiableAt.inner_bundle","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_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.of_eq","ModelProd","ModelWithCorners","ModelWithCorners.prod","Module.toDistribMulAction","Monoid.toNPow","MulZeroClass.toZero","NPow.toPow","Nat","Nat.instCommSemiring","Nat.rawCast","Neg.neg","NegZeroClass.toNeg","NegZeroClass.toZero","NonAssocSemiring.toAddCommMonoidWithOne","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring","NonUnitalNonAssocSemiring.toDistribSMul","NonUnitalNormedCommRing.toNonUnitalNormedRing","NonUnitalNormedRing.toNormedAddCommGroup","NontriviallyNormedField.toNormedField","NormedAddCommGroup","NormedAddCommGroup.toAddCommGroup","NormedAddCommGroup.toSeminormedAddCommGroup","NormedCommRing.toNonUnitalNormedCommRing","NormedCommRing.toSeminormedCommRing","NormedDivisionRing.to_isTopologicalDivisionRing","NormedField.toField","NormedField.toNormedCommRing","NormedField.toNormedDivisionRing","NormedField.toNormedSpace","NormedSpace","NormedSpace.toIsBoundedSMul","NormedSpace.toModule","OfNat.ofNat","One.toOfNat1","Pi.instAdd","Pi.smul'","Prod","Prod.normedAddCommGroup","Prod.normedSpace","PseudoMetricSpace.toUniformSpace","RCLike.toDenselyNormedField","RCLike.toInnerProductSpaceReal","Real","Real.commRing","Real.denselyNormedField","Real.instAdd","Real.instAddCommGroup","Real.instAddCommMonoid","Real.instCommSemiring","Real.instMonoid","Real.instMul","Real.instRCLike","Real.instRing","Real.instSub","Real.instZero","Real.normedAddCommGroup","Real.normedField","Real.pseudoMetricSpace","Real.semiring","Ring","Ring.toAddCommGroup","Ring.toSemiring","RingHom.id","SMulZeroClass.toSMul","Semifield.toCommSemiring","Semifield.toDivisionSemiring","SeminormedAddCommGroup.toAddCommGroup","SeminormedAddCommGroup.toIsTopologicalAddGroup","SeminormedAddCommGroup.toPseudoMetricSpace","SeminormedCommRing.toSeminormedRing","SeminormedRing.toPseudoMetricSpace","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toMonoid","Semiring.toNonAssocSemiring","SeparatelyContinuousMul.to_continuousSMul","SubNegMonoid.toAddMonoid","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegZeroMonoid","TangentSpace","TensorialAt.mk","TopologicalSpace","True","True.intro","UniformSpace.toTopologicalSpace","VectorBundle","WithTop","WithTop.one","Zero.toOfNat0","_private.Mathlib.Geometry.Manifold.VectorBundle.CovariantDerivative.Metric.0.CovariantDerivative.derivMetricTensorAux","_private.Mathlib.Geometry.Manifold.VectorBundle.CovariantDerivative.Metric.0.CovariantDerivative.derivMetricTensorAux_apply","_private.Mathlib.Geometry.Manifold.VectorBundle.CovariantDerivative.Metric.0.CovariantDerivative.tensorial_derivMetricTensorAux₂._abel_1_1","add_apply","chartedSpaceSelf","congr","congrArg","congrFun","congrFun'","funext","id","inferInstance","inner_add_right","inner_smul_right","instAddCommGroupTangentSpace","instAddMonoidWithOneENat","instDistribOfSemiring","instHAdd","instHMul","instHPow","instHSMul","instHSub","instIsTopologicalAddGroupReal","instIsTopologicalRingReal","instModuleTangentSpace","instMulZeroClassOfSemiring","instSMulOfMul","instTopologicalSpaceModelProd","instTopologicalSpaceTangentSpace","modelWithCornersSelf","mvfderiv","mvfderiv_fun_add","mvfderiv_fun_mul","rfl","smulCommClass_self","smul_apply"]} 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ocSemiring","SetLike.instMembership","StarAddMonoid.toInvolutiveStar","StarModule","StarModule.complexToReal","StarRing","StarRing.toStarAddMonoid","SubNegMonoid.toAddMonoid","SubNegMonoid.toNeg","SubNegZeroMonoid.toNegZeroClass","SubtractionCommMonoid.toSubtractionMonoid","SubtractionMonoid.toSubNegMonoid","SubtractionMonoid.toSubNegZeroMonoid","Subtype","Subtype.val","Zero.toOfNat0","add_zero","imaginaryPart","instDistribOfSemiring","instHAdd","instHMul","instHSMul","instOfNat","instOfNatNat","instStarRingReal","instTrivialStarReal","neg_zero","realPart","selfAdjoint","selfAdjoint.instModuleSubtypeMemAddSubgroupOfStarModule","zero_add"]} 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