ContinuousAlternatingMap

📁 Source: Mathlib/Analysis/Calculus/FDeriv/ContinuousAlternatingMap.lean

Statistics

Metric	Count
Definitions ContinuousAlternatingMap	1
Theorems differentiable, hasFDerivAt, hasFDerivWithinAt, hasStrictFDerivAt, hasStrictFDerivAt_compContinuousLinearMap, hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, continuousAlternatingMap_apply, continuousAlternatingMapCompContinuousLinearMap, continuousAlternatingMap_apply, continuousAlternatingMap_apply, continuousAlternatingMapCompContinuousLinearMap, continuousAlternatingMap_apply, continuousAlternatingMapCompContinuousLinearMap, continuousAlternatingMap_apply, continuousAlternatingMapCompContinuousLinearMap, continuousAlternatingMap_apply, continuousAlternatingMapCompContinuousLinearMap, continuousAlternatingMap_apply, fderivWithin_continuousAlternatingMapCompContinuousLinearMap, fderivWithin_continuousAlternatingMap_apply, fderivWithin_continuousAlternatingMap_apply_apply, fderiv_continuousAlternatingMapCompContinuousLinearMap, fderiv_continuousAlternatingMap_apply, fderiv_continuousAlternatingMap_apply_apply	24
Total	25

ContinuousAlternatingMap

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
differentiable 📖	mathematical	—	Differentiable Pi.addCommGroup NormedAddCommGroup.toAddCommGroup Pi.Function.module DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField ESeminormedAddCommMonoid.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule Pi.topologicalSpace DFunLike.coe ContinuousAlternatingMap funLike	—	nonempty_fintype Differentiable.continuousAlternatingMap_apply differentiable_const SeminormedAddCommGroup.toIsTopologicalAddGroup UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self differentiable_apply
hasFDerivAt 📖	mathematical	—	HasFDerivAt Pi.addCommGroup NormedAddCommGroup.toAddCommGroup Pi.module DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField ESeminormedAddCommMonoid.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule Pi.topologicalSpace DFunLike.coe ContinuousAlternatingMap funLike ContinuousMultilinearMap.linearDeriv toContinuousMultilinearMap IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup SeminormedAddCommGroup.toIsTopologicalAddGroup	—	ContinuousMultilinearMap.hasFDerivAt
hasFDerivWithinAt 📖	mathematical	—	HasFDerivWithinAt Pi.addCommGroup NormedAddCommGroup.toAddCommGroup Pi.module DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField ESeminormedAddCommMonoid.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule Pi.topologicalSpace DFunLike.coe ContinuousAlternatingMap funLike ContinuousMultilinearMap.linearDeriv toContinuousMultilinearMap IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup SeminormedAddCommGroup.toIsTopologicalAddGroup	—	HasFDerivAt.hasFDerivWithinAt IsTopologicalAddGroup.toContinuousAdd SeminormedAddCommGroup.toIsTopologicalAddGroup hasFDerivAt
hasStrictFDerivAt 📖	mathematical	—	HasStrictFDerivAt Pi.addCommGroup NormedAddCommGroup.toAddCommGroup Pi.module DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField ESeminormedAddCommMonoid.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule Pi.topologicalSpace DFunLike.coe ContinuousAlternatingMap funLike ContinuousMultilinearMap.linearDeriv toContinuousMultilinearMap IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup SeminormedAddCommGroup.toIsTopologicalAddGroup	—	ContinuousMultilinearMap.hasStrictFDerivAt
hasStrictFDerivAt_compContinuousLinearMap 📖	mathematical	—	HasStrictFDerivAt ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField ESeminormedAddCommMonoid.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring Prod.instAddCommGroup instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing NormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.addCommGroup Prod.instModule AddCommGroup.toAddCommMonoid SeminormedAddCommGroup.toAddCommGroup addCommMonoid IsTopologicalAddGroup.toContinuousAdd AddCommGroup.toAddGroup ContinuousLinearMap.addCommMonoid SeminormedAddGroup.toAddGroup SeminormedAddCommGroup.toSeminormedAddGroup instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousLinearMap.module instTopologicalSpaceProd instTopologicalSpace ContinuousLinearMap.topologicalSpace compContinuousLinearMap Prod.instAddCommMonoid ContinuousLinearMap.add NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup instNormedAddCommGroup instIsTopologicalAddGroup ContinuousLinearMap.comp RingHomCompTriple.ids compContinuousLinearMapCLM ContinuousLinearMap.fst fderivCompContinuousLinearMap ContinuousLinearMap.snd	—	SeminormedAddCommGroup.toIsTopologicalAddGroup IsTopologicalAddGroup.toContinuousAdd UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self instIsTopologicalAddGroup RingHomCompTriple.ids RingHomIsometric.ids hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff Finite.of_fintype ContinuousMultilinearMap.instIsTopologicalAddGroup ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap ContinuousLinearMap.hasStrictFDerivAt hasStrictFDerivAt_pi hasStrictFDerivAt_id HasStrictFDerivAt.comp HasStrictFDerivAt.prodMap
hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff 📖	mathematical	—	HasStrictFDerivAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousMultilinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousMultilinearMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousMultilinearMap.instModule AddCommGroup.toAddCommMonoid IsTopologicalAddGroup.toContinuousAdd AddCommGroup.toAddGroup UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Ring.toSemiring CommRing.toRing ContinuousMultilinearMap.instTopologicalSpace ContinuousAlternatingMap toContinuousMultilinearMap ContinuousLinearMap.comp RingHom.id Semiring.toNonAssocSemiring instTopologicalSpace addCommMonoid instModule RingHomCompTriple.ids toContinuousMultilinearMapCLM instAddCommGroup NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup	—	SeminormedAddCommGroup.toIsTopologicalAddGroup IsTopologicalAddGroup.toContinuousAdd UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self nonempty_fintype RingHomCompTriple.ids hasStrictFDerivAt_iff_isLittleOTVS Asymptotics.IsBigOTVS.trans_isLittleOTVS toContinuousMultilinearMapCLM_apply DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass ContinuousLinearMap.continuousSemilinearMapClass LinearMap.isBigOTVS_rev_comp Topology.IsInducing.nhds_eq_comap Topology.IsEmbedding.toIsInducing isEmbedding_toContinuousMultilinearMap instReflLe HasStrictFDerivAt.comp SeminormedAddCommGroup.to_isUniformAddGroup ContinuousLinearMap.hasStrictFDerivAt

Differentiable

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
continuousAlternatingMap_apply 📖	mathematical	Differentiable NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace	Differentiable NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace DFunLike.coe ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.funLike	—	SeminormedAddCommGroup.toIsTopologicalAddGroup UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self DifferentiableAt.continuousAlternatingMap_apply

DifferentiableAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
continuousAlternatingMapCompContinuousLinearMap 📖	mathematical	DifferentiableAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring ContinuousLinearMap.addCommGroup ContinuousLinearMap.module ContinuousLinearMap.topologicalSpace	DifferentiableAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace ContinuousAlternatingMap.compContinuousLinearMap	—	SeminormedAddCommGroup.toIsTopologicalAddGroup UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self nonempty_fintype HasFDerivAt.differentiableAt IsTopologicalAddGroup.toContinuousAdd ContinuousAlternatingMap.instIsTopologicalAddGroup RingHomCompTriple.ids HasFDerivAt.continuousAlternatingMapCompContinuousLinearMap hasFDerivAt
continuousAlternatingMap_apply 📖	mathematical	DifferentiableAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace	DifferentiableAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace DFunLike.coe ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.funLike	—	SeminormedAddCommGroup.toIsTopologicalAddGroup UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self nonempty_fintype HasFDerivAt.differentiableAt IsTopologicalAddGroup.toContinuousAdd RingHomCompTriple.ids IsBoundedSMul.continuousSMul HasFDerivAt.continuousAlternatingMap_apply hasFDerivAt

DifferentiableOn

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
continuousAlternatingMap_apply 📖	mathematical	DifferentiableOn NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace	DifferentiableOn NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace DFunLike.coe ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.funLike	—	SeminormedAddCommGroup.toIsTopologicalAddGroup UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self DifferentiableWithinAt.continuousAlternatingMap_apply

DifferentiableWithinAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
continuousAlternatingMapCompContinuousLinearMap 📖	mathematical	DifferentiableWithinAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring ContinuousLinearMap.addCommGroup ContinuousLinearMap.module ContinuousLinearMap.topologicalSpace	DifferentiableWithinAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace ContinuousAlternatingMap.compContinuousLinearMap	—	SeminormedAddCommGroup.toIsTopologicalAddGroup UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self nonempty_fintype HasFDerivWithinAt.differentiableWithinAt IsTopologicalAddGroup.toContinuousAdd ContinuousAlternatingMap.instIsTopologicalAddGroup RingHomCompTriple.ids HasFDerivWithinAt.continuousAlternatingMapCompContinuousLinearMap hasFDerivWithinAt
continuousAlternatingMap_apply 📖	mathematical	DifferentiableWithinAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace	DifferentiableWithinAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace DFunLike.coe ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.funLike	—	SeminormedAddCommGroup.toIsTopologicalAddGroup UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self nonempty_fintype HasFDerivWithinAt.differentiableWithinAt IsTopologicalAddGroup.toContinuousAdd RingHomCompTriple.ids IsBoundedSMul.continuousSMul HasFDerivWithinAt.continuousAlternatingMap_apply hasFDerivWithinAt

HasFDerivAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
continuousAlternatingMapCompContinuousLinearMap 📖	mathematical	HasFDerivAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring ContinuousLinearMap.addCommGroup ContinuousLinearMap.module ContinuousLinearMap.topologicalSpace	HasFDerivAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule AddCommGroup.toAddCommMonoid IsTopologicalAddGroup.toContinuousAdd AddCommGroup.toAddGroup UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace ContinuousAlternatingMap.compContinuousLinearMap ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring ContinuousAlternatingMap.addCommMonoid SeminormedAddCommGroup.toAddCommGroup SeminormedAddGroup.toAddGroup SeminormedAddCommGroup.toSeminormedAddGroup ContinuousLinearMap.add NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup ContinuousAlternatingMap.instNormedAddCommGroup ContinuousAlternatingMap.instIsTopologicalAddGroup ContinuousLinearMap.comp RingHomCompTriple.ids ContinuousAlternatingMap.compContinuousLinearMapCLM ContinuousLinearMap.topologicalSpace ContinuousLinearMap.addCommMonoid ContinuousLinearMap.module ContinuousAlternatingMap.fderivCompContinuousLinearMap	—	SeminormedAddCommGroup.toIsTopologicalAddGroup IsTopologicalAddGroup.toContinuousAdd UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self ContinuousAlternatingMap.instIsTopologicalAddGroup RingHomCompTriple.ids RingHomIsometric.ids comp HasStrictFDerivAt.hasFDerivAt ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap prodMk
continuousAlternatingMap_apply 📖	mathematical	HasFDerivAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace	HasFDerivAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace DFunLike.coe ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.funLike ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.add IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.comp ContinuousAlternatingMap.instTopologicalSpace ContinuousAlternatingMap.addCommMonoid AddCommGroup.toAddGroup ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Ring.toSemiring CommRing.toRing RingHomCompTriple.ids ContinuousAlternatingMap.apply IsBoundedSMul.continuousSMul Finset.sum ContinuousLinearMap.addCommMonoid Finset.univ ContinuousAlternatingMap.toContinuousLinearMap	—	SeminormedAddCommGroup.toIsTopologicalAddGroup IsTopologicalAddGroup.toContinuousAdd UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self continuousMultilinearMap_apply SeminormedAddCommGroup.to_isUniformAddGroup RingHomCompTriple.ids comp ContinuousLinearMap.hasFDerivAt

HasFDerivWithinAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
continuousAlternatingMapCompContinuousLinearMap 📖	mathematical	HasFDerivWithinAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring ContinuousLinearMap.addCommGroup ContinuousLinearMap.module ContinuousLinearMap.topologicalSpace	HasFDerivWithinAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule AddCommGroup.toAddCommMonoid IsTopologicalAddGroup.toContinuousAdd AddCommGroup.toAddGroup UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace ContinuousAlternatingMap.compContinuousLinearMap ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring ContinuousAlternatingMap.addCommMonoid SeminormedAddCommGroup.toAddCommGroup SeminormedAddGroup.toAddGroup SeminormedAddCommGroup.toSeminormedAddGroup ContinuousLinearMap.add NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup ContinuousAlternatingMap.instNormedAddCommGroup ContinuousAlternatingMap.instIsTopologicalAddGroup ContinuousLinearMap.comp RingHomCompTriple.ids ContinuousAlternatingMap.compContinuousLinearMapCLM ContinuousLinearMap.topologicalSpace ContinuousLinearMap.addCommMonoid ContinuousLinearMap.module ContinuousAlternatingMap.fderivCompContinuousLinearMap	—	SeminormedAddCommGroup.toIsTopologicalAddGroup IsTopologicalAddGroup.toContinuousAdd UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self ContinuousAlternatingMap.instIsTopologicalAddGroup RingHomCompTriple.ids RingHomIsometric.ids HasFDerivAt.comp_hasFDerivWithinAt HasStrictFDerivAt.hasFDerivAt ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap prodMk
continuousAlternatingMap_apply 📖	mathematical	HasFDerivWithinAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace	HasFDerivWithinAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace DFunLike.coe ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.funLike ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.add IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.comp ContinuousAlternatingMap.instTopologicalSpace ContinuousAlternatingMap.addCommMonoid AddCommGroup.toAddGroup ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Ring.toSemiring CommRing.toRing RingHomCompTriple.ids ContinuousAlternatingMap.apply IsBoundedSMul.continuousSMul Finset.sum ContinuousLinearMap.addCommMonoid Finset.univ ContinuousAlternatingMap.toContinuousLinearMap	—	SeminormedAddCommGroup.toIsTopologicalAddGroup IsTopologicalAddGroup.toContinuousAdd UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self continuousMultilinearMap_apply SeminormedAddCommGroup.to_isUniformAddGroup RingHomCompTriple.ids HasFDerivAt.comp_hasFDerivWithinAt ContinuousLinearMap.hasFDerivAt

HasStrictFDerivAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
continuousAlternatingMapCompContinuousLinearMap 📖	mathematical	HasStrictFDerivAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring ContinuousLinearMap.addCommGroup ContinuousLinearMap.module ContinuousLinearMap.topologicalSpace	HasStrictFDerivAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule AddCommGroup.toAddCommMonoid IsTopologicalAddGroup.toContinuousAdd AddCommGroup.toAddGroup UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace ContinuousAlternatingMap.compContinuousLinearMap ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring ContinuousAlternatingMap.addCommMonoid SeminormedAddCommGroup.toAddCommGroup SeminormedAddGroup.toAddGroup SeminormedAddCommGroup.toSeminormedAddGroup ContinuousLinearMap.add NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup ContinuousAlternatingMap.instNormedAddCommGroup ContinuousAlternatingMap.instIsTopologicalAddGroup ContinuousLinearMap.comp RingHomCompTriple.ids ContinuousAlternatingMap.compContinuousLinearMapCLM ContinuousLinearMap.topologicalSpace ContinuousLinearMap.addCommMonoid ContinuousLinearMap.module ContinuousAlternatingMap.fderivCompContinuousLinearMap	—	SeminormedAddCommGroup.toIsTopologicalAddGroup IsTopologicalAddGroup.toContinuousAdd UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self comp RingHomIsometric.ids ContinuousAlternatingMap.instIsTopologicalAddGroup RingHomCompTriple.ids ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap prodMk
continuousAlternatingMap_apply 📖	mathematical	HasStrictFDerivAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace	HasStrictFDerivAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace DFunLike.coe ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.funLike ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.add IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.comp ContinuousAlternatingMap.instTopologicalSpace ContinuousAlternatingMap.addCommMonoid AddCommGroup.toAddGroup ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Ring.toSemiring CommRing.toRing RingHomCompTriple.ids ContinuousAlternatingMap.apply IsBoundedSMul.continuousSMul Finset.sum ContinuousLinearMap.addCommMonoid Finset.univ ContinuousAlternatingMap.toContinuousLinearMap	—	SeminormedAddCommGroup.toIsTopologicalAddGroup IsTopologicalAddGroup.toContinuousAdd UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self continuousMultilinearMap_apply SeminormedAddCommGroup.to_isUniformAddGroup RingHomCompTriple.ids comp ContinuousLinearMap.hasStrictFDerivAt

(root)

Definitions

Name	Category	Theorems
ContinuousAlternatingMap 📖	CompData	262 math math: ContinuousAlternatingMap.cons_add, extDerivWithin_fun_add, ContinuousAlternatingMap.opNorm_prod, ContinuousAlternatingMap.uniformContinuous_eval_const, LinearIsometry.norm_compContinuousAlternatingMap, extDeriv_constOfIsEmpty, ContinuousAlternatingMap.isEmbedding_restrictScalars, ContinuousAlternatingMap.norm_constOfIsEmpty, ContinuousAlternatingMap.norm_ofSubsingleton_id_le, ContinuousAlternatingMap.isClosedEmbedding_toContinuousMultilinearMap, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, ContinuousAlternatingMap.isUniformEmbedding_toContinuousMultilinearMap, ContinuousMultilinearMap.alternatization_apply_apply, ContinuousAlternatingMap.instIsUniformAddGroup, ContinuousAlternatingMap.vecCons_smul, ContinuousAlternatingMap.opNNNorm_pi, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, ContinuousAlternatingMap.tsum_eval, ContinuousAlternatingMap.map_insertNth, ContinuousAlternatingMap.le_mul_prod_of_opNorm_le_of_le, fderiv_continuousAlternatingMap_apply_const, DifferentiableAt.continuousAlternatingMapCompContinuousLinearMap, ContinuousAlternatingMap.isClosed_range_toContinuousMultilinearMap, ContinuousAlternatingMap.smul_apply, ContinuousAlternatingMap.compContinuousLinearMapₗ_apply, ContinuousAlternatingMap.piLIE_apply_apply, ContinuousAlternatingMap.coe_pi, ContinuousAlternatingMap.toAlternatingMapLinear_apply, ContinuousAlternatingMap.norm_def, ContinuousAlternatingMap.curryLeft_smul, ContinuousAlternatingMap.map_coord_zero, HasFDerivWithinAt.continuousAlternatingMap_apply, ContinuousAlternatingMap.toAlternatingMap_injective, extDeriv_fun_smul, ContinuousAlternatingMap.toAlternatingMap_curryLeft, ContinuousAlternatingMap.piEquiv_apply, ContinuousAlternatingMap.le_opNNNorm, ContinuousAlternatingMap.hasSum_eval, ContinuousAlternatingMap.constOfIsEmptyLIE_apply, DifferentiableAt.continuousAlternatingMap_apply_const, fderiv_continuousAlternatingMapCompContinuousLinearMap, ContinuousLinearEquiv.continuousAlternatingMapCongrLeftEquiv_apply, ContinuousAlternatingMap.instContinuousSMul, extDerivWithin_constOfIsEmpty, ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply, fderiv_continuousAlternatingMap_apply, ContinuousAlternatingMap.instContinuousConstSMul, ContinuousAlternatingMap.ofSubsingleton_apply_toContinuousMultilinearMap, ContinuousLinearEquiv.compContinuousAlternatingMap_coe, extDerivWithin_add, HasFDerivAt.continuousAlternatingMap_apply, AlternatingMap.coe_mkContinuous, ContinuousAlternatingMap.curryLeft_apply_apply, ContinuousAlternatingMap.coe_smul, ContinuousAlternatingMap.isEmbedding_toContinuousMultilinearMap, fderivWithin_continuousAlternatingMap_apply_const_apply, ContinuousAlternatingMap.isUniformInducing_postcomp, DifferentiableWithinAt.continuousAlternatingMap_apply_const, ContinuousAlternatingMap.alternatizeUncurryFin_smul, extDeriv_apply_vectorField, ContinuousAlternatingMap.norm_restrictScalars, ContinuousAlternatingMap.isUniformEmbedding_restrictScalars, ContinuousAlternatingMap.coe_sub, ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, ContinuousAlternatingMap.map_piecewise_smul, ContinuousAlternatingMap.continuous_compContinuousLinearMapCLM, ContinuousAlternatingMap.instIsTopologicalAddGroup, ContinuousAlternatingMap.map_update_sub, extDeriv_extDeriv, ContinuousAlternatingMap.le_opNorm, ContinuousAlternatingMap.map_update_add, ContinuousAlternatingMap.piEquiv_symm_apply, DifferentiableWithinAt.continuousAlternatingMapCompContinuousLinearMap, ContinuousAlternatingMap.norm_curryLeft, ContinuousAlternatingMap.apply_apply, fderivWithin_continuousAlternatingMapCompContinuousLinearMap, extDerivWithin_extDerivWithin_eqOn, ContinuousAlternatingMap.add_apply, ContinuousAlternatingMap.map_sum, ContinuousAlternatingMap.instUniformContinuousConstSMul, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, AlternatingMap.mkContinuousAlternating_norm_le, ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap, ContinuousAlternatingMap.toAlternatingMap_smul, AlternatingMap.mkContinuous_norm_le, ContinuousAlternatingMap.ofSubsingletonLIE_apply, ContinuousAlternatingMap.map_sum_finset, extDerivWithin_apply_vectorField_of_pairwise_commute, ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply, ContinuousAlternatingMap.map_zero, ContinuousAlternatingMap.norm_ofSubsingleton, ContinuousAlternatingMap.sub_apply, ContinuousAlternatingMap.toContinuousMultilinearMap_zero, ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply, ContinuousAlternatingMap.hasStrictFDerivAt, ContinuousAlternatingMap.map_update_smul, DifferentiableAt.continuousAlternatingMap_apply, extDerivWithin_fun_smul, HasFDerivWithinAt.continuousAlternatingMapCompContinuousLinearMap, ContinuousAlternatingMap.range_toContinuousMultilinearMap, ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin, ContinuousAlternatingMap.le_opNorm_mul_pow_of_le, ContinuousAlternatingMap.curryLeft_compContinuousLinearMap, ContinuousAlternatingMap.norm_toContinuousMultilinearMap, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_symm, ContinuousAlternatingMap.isLeast_opNorm, ContinuousAlternatingMap.toContinuousMultilinearMapLinear_apply, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_apply, Filter.EventuallyEq.extDerivWithin', extDeriv_smul, ContinuousAlternatingMap.prod_apply, ContinuousAlternatingMap.pi_apply, ContinuousLinearMap.compContinuousAlternatingMap_coe, HasFDerivAt.continuousAlternatingMap_apply_const, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin, ContinuousAlternatingMap.hasBasis_nhds_zero, DifferentiableOn.continuousAlternatingMap_apply, ContinuousAlternatingMap.uniformContinuous_coe_fun, extDeriv_add, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap, extDerivWithin_apply_vectorField, ContinuousAlternatingMap.sum_apply, ContinuousAlternatingMap.nnnorm_ofSubsingleton_id, ContinuousAlternatingMap.continuous_restrictScalars, ContinuousAlternatingMap.map_add_univ, ContinuousAlternatingMap.ext_iff, HasStrictFDerivAt.continuousAlternatingMap_apply, ContinuousAlternatingMap.toAlternatingMap_zero, ContinuousAlternatingMap.instT3Space, ContinuousAlternatingMap.curryLeft_same, ContinuousAlternatingMap.curryLeft_zero, ContinuousAlternatingMap.completeSpace, ContinuousAlternatingMap.restrictScalarsLI_apply, ContinuousAlternatingMap.cons_smul, ContinuousAlternatingMap.vecCons_add, ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft, ContinuousAlternatingMap.norm_image_sub_le', ContinuousAlternatingMap.uniformContinuous_toContinuousMultilinearMap, ContinuousAlternatingMap.piLIE_symm_apply_apply, ContinuousAlternatingMap.le_opNorm_mul_pow_card_of_le, ContinuousAlternatingMap.piLinearEquiv_symm_apply, fderiv_continuousAlternatingMap_apply_apply, ContinuousAlternatingMap.le_of_opNorm_le, ContinuousAlternatingMap.range_toAlternatingMap, ContinuousAlternatingMap.compContinuousLinearMap_apply, ContinuousAlternatingMap.coe_mk, ContinuousAlternatingMap.toContinuousMultilinearMap_injective, ContinuousAlternatingMap.ofSubsingleton_apply_apply, ContinuousAlternatingMap.restrictScalarsCLM_apply, ContinuousMultilinearMap.alternatization_apply_toContinuousMultilinearMap, Filter.EventuallyEq.extDeriv, fderivWithin_continuousAlternatingMap_apply_apply, ContinuousAlternatingMap.coe_zero, ContinuousLinearMap.norm_compContinuousAlternatingMap_le, ContinuousAlternatingMap.isLeast_opNNNorm, Differentiable.continuousAlternatingMap_apply_const, ContinuousLinearEquiv.continuousAlternatingMapCongrLeft_apply, ContinuousAlternatingMap.map_vecCons_sub, ContinuousAlternatingMap.hasBasis_nhds_zero_of_basis, Filter.EventuallyEq.extDerivWithin, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_apply, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_of_symmetric, ContinuousAlternatingMap.nnnorm_toContinuousMultilinearMap, fderivWithin_continuousAlternatingMap_apply_const, extDeriv_fun_add, extDerivWithin_extDerivWithin_apply, ContinuousAlternatingMap.constOfIsEmpty_apply, ContinuousMultilinearMap.alternatization_apply_toAlternatingMap, ContinuousAlternatingMap.ext_ring_iff, ContinuousAlternatingMap.instCompleteSpace, ContinuousAlternatingMap.map_eq_zero_of_not_injective, ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply, ContinuousAlternatingMap.norm_ofSubsingleton_id, extDerivWithin_smul, ContinuousAlternatingMap.neg_apply, ContinuousAlternatingMap.opNorm_le_iff, ContinuousAlternatingMap.map_piecewise_add, ContinuousAlternatingMap.curryLeft_add, extDeriv_apply_vectorField_of_pairwise_commute, ContinuousAlternatingMap.prodLIE_apply, ContinuousAlternatingMap.coe_toContinuousMultilinearMap, DifferentiableWithinAt.continuousAlternatingMap_apply, ContinuousAlternatingMap.hasFDerivWithinAt, AlternatingMap.mkContinuousLinear_norm_le, ContinuousAlternatingMap.curryLeftLI_apply, ContinuousAlternatingMap.instIsCentralScalar, ContinuousAlternatingMap.map_eq_zero_of_eq, ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty, ContinuousAlternatingMap.neg_one_pow_smul_map_removeNth_add_eq_zero_of_eq, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, ContinuousLinearEquiv.continuousAlternatingMapCongrRightEquiv_apply, ContinuousAlternatingMap.opNorm_le_bound, AlternatingMap.mkContinuousAlternating_norm_le_max, ContinuousAlternatingMap.map_update_zero, HasStrictFDerivAt.continuousAlternatingMap_apply_const, extDeriv_extDeriv_apply, ContinuousLinearEquiv.continuousAlternatingMapCongr_apply, ContinuousAlternatingMap.toAlternatingMap_add, ContinuousAlternatingMap.nnnorm_ofSubsingleton, ContinuousAlternatingMap.toContinuousLinearMap_apply, ContinuousAlternatingMap.alternatizeUncurryFin_add, ContinuousAlternatingMap.codRestrict_apply_coe, ContinuousAlternatingMap.instT2Space, DifferentiableOn.continuousAlternatingMap_apply_const, fderivWithin_continuousAlternatingMap_apply, ContinuousAlternatingMap.differentiable, ContinuousAlternatingMap.continuousMapClass, ContinuousAlternatingMap.coe_neg, ContinuousAlternatingMap.neg_one_pow_smul_map_insertNth, ContinuousAlternatingMap.nnnorm_ofSubsingleton_id_le, ContinuousAlternatingMap.nnnorm_constOfIsEmpty, ContinuousAlternatingMap.instSMulCommClass, ContinuousAlternatingMap.alternatizeUncurryFin_curryLeft, ContinuousLinearMap.compContinuousAlternatingMapCLM_apply_apply, ContinuousAlternatingMap.unit_le_opNorm, extDerivWithin_apply, ContinuousAlternatingMap.opNNNorm_le_iff, ContinuousAlternatingMap.liftCLM_apply, ContinuousAlternatingMap.bound, ContinuousAlternatingMap.toContinuousMultilinearMap_smul, Differentiable.continuousAlternatingMap_apply, ContinuousAlternatingMap.coe_restrictScalars, ContinuousAlternatingMap.map_smul_univ, ContinuousAlternatingMap.toContinuousMultilinearMap_add, ContinuousAlternatingMap.opNorm_pi, ContinuousAlternatingMap.uniformContinuous_restrictScalars, ContinuousAlternatingMap.instContinuousEval, ContinuousAlternatingMap.norm_compContinuousLinearMap_le, ContinuousAlternatingMap.coe_toAlternatingMap, ContinuousAlternatingMap.hasFDerivAt, HasStrictFDerivAt.continuousAlternatingMapCompContinuousLinearMap, ContinuousAlternatingMap.prodLIE_symm_apply, ContinuousAlternatingMap.coe_continuous, AlternatingMap.mkContinuousLinear_norm_le_max, ContinuousAlternatingMap.opNNNorm_prod, fderiv_continuousAlternatingMap_apply_const_apply, HasFDerivAt.continuousAlternatingMapCompContinuousLinearMap, ContinuousAlternatingMap.coe_add, ContinuousAlternatingMap.continuous_toContinuousMultilinearMap, ContinuousAlternatingMap.ofSubsingleton_toAlternatingMap, ContinuousAlternatingMap.alternatizeUncurryFin_fderivCompContinuousLinearMap_eq_zero, ContinuousAlternatingMap.enorm_toContinuousMultilinearMap, ContinuousAlternatingMap.piLinearEquiv_apply, ContinuousAlternatingMap.compContinuousLinearMapCLM_apply, AlternatingMap.mkContinuousAlternating_apply, ContinuousAlternatingMap.instIsScalarTower, ContinuousAlternatingMap.alternatizeUncurryFin_apply, AlternatingMap.mkContinuous_norm_le', ContinuousAlternatingMap.ratio_le_opNorm, ContinuousAlternatingMap.ofSubsingleton_symm_apply_apply, ContinuousAlternatingMap.toMultilinearAddHom_apply, HasFDerivWithinAt.continuousAlternatingMap_apply_const, ContinuousAlternatingMap.instContinuousEvalConst, ContinuousAlternatingMap.norm_image_sub_le, ContinuousAlternatingMap.smulRight_apply, extDeriv_apply, ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, ContinuousAlternatingMap.le_of_opNNNorm_le, ContinuousLinearMap.flipAlternating_apply_apply, ContinuousAlternatingMap.le_opNorm_mul_prod_of_le

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
fderivWithin_continuousAlternatingMapCompContinuousLinearMap 📖	mathematical	DifferentiableWithinAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring ContinuousLinearMap.addCommGroup ContinuousLinearMap.module ContinuousLinearMap.topologicalSpace UniqueDiffWithinAt	fderivWithin NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace ContinuousAlternatingMap.compContinuousLinearMap ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousAlternatingMap.addCommMonoid IsTopologicalAddGroup.toContinuousAdd AddCommGroup.toAddGroup SeminormedAddCommGroup.toAddCommGroup SeminormedAddGroup.toAddGroup SeminormedAddCommGroup.toSeminormedAddGroup ContinuousLinearMap.add NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup ContinuousAlternatingMap.instNormedAddCommGroup ContinuousAlternatingMap.instIsTopologicalAddGroup ContinuousLinearMap.comp RingHomCompTriple.ids ContinuousAlternatingMap.compContinuousLinearMapCLM ContinuousLinearMap.topologicalSpace ContinuousLinearMap.addCommMonoid ContinuousLinearMap.module ContinuousAlternatingMap.fderivCompContinuousLinearMap ContinuousLinearMap.addCommGroup	—	SeminormedAddCommGroup.toIsTopologicalAddGroup UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self HasFDerivWithinAt.fderivWithin IsTopologicalAddGroup.toContinuousAdd ContinuousAlternatingMap.instIsTopologicalAddGroup RingHomCompTriple.ids IsBoundedSMul.continuousSMul ContinuousAlternatingMap.instContinuousSMul ContinuousAlternatingMap.instT2Space TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace HasFDerivWithinAt.continuousAlternatingMapCompContinuousLinearMap DifferentiableWithinAt.hasFDerivWithinAt
fderivWithin_continuousAlternatingMap_apply 📖	mathematical	DifferentiableWithinAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace UniqueDiffWithinAt	fderivWithin NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace DFunLike.coe ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.funLike ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.add IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.comp ContinuousAlternatingMap.instTopologicalSpace ContinuousAlternatingMap.addCommMonoid AddCommGroup.toAddGroup ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Ring.toSemiring CommRing.toRing RingHomCompTriple.ids ContinuousAlternatingMap.apply IsBoundedSMul.continuousSMul ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing Finset.sum ContinuousLinearMap.addCommMonoid Finset.univ ContinuousAlternatingMap.toContinuousLinearMap	—	SeminormedAddCommGroup.toIsTopologicalAddGroup UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self HasFDerivWithinAt.fderivWithin IsTopologicalAddGroup.toContinuousAdd RingHomCompTriple.ids IsBoundedSMul.continuousSMul TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace HasFDerivWithinAt.continuousAlternatingMap_apply DifferentiableWithinAt.hasFDerivWithinAt
fderivWithin_continuousAlternatingMap_apply_apply 📖	mathematical	DifferentiableWithinAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace UniqueDiffWithinAt	DFunLike.coe ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField RingHom.id Semiring.toNonAssocSemiring UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup AddCommGroup.toAddCommMonoid NormedAddCommGroup.toAddCommGroup NormedSpace.toModule ContinuousLinearMap.funLike fderivWithin ContinuousAlternatingMap ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.funLike AddCommMagma.toAdd AddCommSemigroup.toAddCommMagma AddCommMonoid.toAddCommSemigroup ContinuousAlternatingMap.instTopologicalSpace SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing Finset.sum Finset.univ Function.update	—	SeminormedAddCommGroup.toIsTopologicalAddGroup UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self IsTopologicalAddGroup.toContinuousAdd RingHomCompTriple.ids IsBoundedSMul.continuousSMul fderivWithin_continuousAlternatingMap_apply ContinuousLinearMap.coe_sum' Finset.sum_congr Finset.sum_apply
fderiv_continuousAlternatingMapCompContinuousLinearMap 📖	mathematical	DifferentiableAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring ContinuousLinearMap.addCommGroup ContinuousLinearMap.module ContinuousLinearMap.topologicalSpace	fderiv NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace ContinuousAlternatingMap.compContinuousLinearMap ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousAlternatingMap.addCommMonoid IsTopologicalAddGroup.toContinuousAdd AddCommGroup.toAddGroup SeminormedAddCommGroup.toAddCommGroup SeminormedAddGroup.toAddGroup SeminormedAddCommGroup.toSeminormedAddGroup ContinuousLinearMap.add NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup ContinuousAlternatingMap.instNormedAddCommGroup ContinuousAlternatingMap.instIsTopologicalAddGroup ContinuousLinearMap.comp RingHomCompTriple.ids ContinuousAlternatingMap.compContinuousLinearMapCLM ContinuousLinearMap.topologicalSpace ContinuousLinearMap.addCommMonoid ContinuousLinearMap.module ContinuousAlternatingMap.fderivCompContinuousLinearMap ContinuousLinearMap.addCommGroup	—	SeminormedAddCommGroup.toIsTopologicalAddGroup UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self HasFDerivAt.fderiv IsTopologicalAddGroup.toContinuousAdd ContinuousAlternatingMap.instIsTopologicalAddGroup RingHomCompTriple.ids IsBoundedSMul.continuousSMul ContinuousAlternatingMap.instContinuousSMul ContinuousAlternatingMap.instT2Space TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace HasFDerivAt.continuousAlternatingMapCompContinuousLinearMap DifferentiableAt.hasFDerivAt
fderiv_continuousAlternatingMap_apply 📖	mathematical	DifferentiableAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace	fderiv NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace DFunLike.coe ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.funLike ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.add IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.comp ContinuousAlternatingMap.instTopologicalSpace ContinuousAlternatingMap.addCommMonoid AddCommGroup.toAddGroup ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Ring.toSemiring CommRing.toRing RingHomCompTriple.ids ContinuousAlternatingMap.apply IsBoundedSMul.continuousSMul ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing Finset.sum ContinuousLinearMap.addCommMonoid Finset.univ ContinuousAlternatingMap.toContinuousLinearMap	—	SeminormedAddCommGroup.toIsTopologicalAddGroup UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self HasFDerivAt.fderiv IsTopologicalAddGroup.toContinuousAdd RingHomCompTriple.ids IsBoundedSMul.continuousSMul TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace HasFDerivAt.continuousAlternatingMap_apply DifferentiableAt.hasFDerivAt
fderiv_continuousAlternatingMap_apply_apply 📖	mathematical	DifferentiableAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ContinuousAlternatingMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing ContinuousAlternatingMap.instTopologicalSpace	DFunLike.coe ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField RingHom.id Semiring.toNonAssocSemiring UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup AddCommGroup.toAddCommMonoid NormedAddCommGroup.toAddCommGroup NormedSpace.toModule ContinuousLinearMap.funLike fderiv ContinuousAlternatingMap ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousAlternatingMap.funLike AddCommMagma.toAdd AddCommSemigroup.toAddCommMagma AddCommMonoid.toAddCommSemigroup ContinuousAlternatingMap.instTopologicalSpace SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousAlternatingMap.instAddCommGroup NormedRing.toRing NormedCommRing.toNormedRing NormedField.toNormedCommRing ContinuousAlternatingMap.instModule UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction IsBoundedSMul.toUniformContinuousConstSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedSpace.toIsBoundedSMul smulCommClass_self CommRing.toCommMonoid Field.toCommRing DistribMulAction.toMulAction CommMonoid.toMonoid Ring.toSemiring CommRing.toRing Finset.sum Finset.univ Function.update	—	SeminormedAddCommGroup.toIsTopologicalAddGroup UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self IsTopologicalAddGroup.toContinuousAdd RingHomCompTriple.ids IsBoundedSMul.continuousSMul fderiv_continuousAlternatingMap_apply ContinuousLinearMap.coe_sum' Finset.sum_congr Finset.sum_apply

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