Documentation Verification Report

ContinuousMultilinearMap

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

Statistics

MetricCount
DefinitionsContinuousMultilinearMap
1
TheoremshasStrictFDerivAt_compContinuousLinearMap, continuousMultilinearMapCompContinuousLinearMap, continuousMultilinearMapCompContinuousLinearMap, continuousMultilinearMapCompContinuousLinearMap, continuousMultilinearMapCompContinuousLinearMap, continuousMultilinearMapCompContinuousLinearMap, continuousMultilinearMapCompContinuousLinearMap, continuousMultilinearMapCompContinuousLinearMap, fderivWithin_continuousMultilinearMapCompContinuousLinearMap, fderiv_continuousMultilinearMapCompContinuousLinearMap
10
Total11

ContinuousMultilinearMap

Theorems

NameKindAssumesProvesValidatesDepends On
hasStrictFDerivAt_compContinuousLinearMap 📖mathematicalHasStrictFDerivAt
ContinuousMultilinearMap
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
Prod.instAddCommGroup
instAddCommGroup
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
NormedAddCommGroup.toAddCommGroup
SeminormedAddCommGroup.toAddCommGroup
SeminormedAddCommGroup.toIsTopologicalAddGroup
Pi.addCommGroup
ContinuousLinearMap
RingHom.id
Semiring.toNonAssocSemiring
ContinuousLinearMap.addCommGroup
Prod.instModule
AddCommGroup.toAddCommMonoid
addCommMonoid
IsTopologicalAddGroup.toContinuousAdd
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
Pi.addCommMonoid
ContinuousLinearMap.addCommMonoid
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
Pi.module
ContinuousLinearMap.module
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instTopologicalSpaceProd
instTopologicalSpace
Pi.topologicalSpace
ContinuousLinearMap.topologicalSpace
compContinuousLinearMap
Prod.instAddCommMonoid
ContinuousLinearMap.add
NormedAddGroup.toAddGroup
NormedAddCommGroup.toNormedAddGroup
normedAddCommGroup
instIsTopologicalAddGroup
ContinuousLinearMap.comp
RingHomCompTriple.ids
compContinuousLinearMapL
ContinuousLinearMap.fst
fderivCompContinuousLinearMap
ContinuousLinearMap.snd
RingHomIsometric.ids
smulCommClass_self
SeminormedAddCommGroup.toIsTopologicalAddGroup
IsTopologicalAddGroup.toContinuousAdd
UniformContinuousConstSMul.to_continuousConstSMul
IsBoundedSMul.toUniformContinuousConstSMul
NormedSpace.toIsBoundedSMul
instSMulCommClass
hasStrictFDerivAt
instIsTopologicalAddGroup
RingHomCompTriple.ids
ContinuousLinearMap.prod_ext
ContinuousLinearMap.ext
ext
linearDeriv_apply
Finset.sum_congr
ContinuousLinearMap.compContinuousMultilinearMap_coe
sum_apply
ContinuousLinearMap.coe_sum'
Finset.sum_apply
HasStrictFDerivAt.clm_apply
HasStrictFDerivAt.comp
hasStrictFDerivAt_snd
hasStrictFDerivAt_fst

Differentiable

Theorems

NameKindAssumesProvesValidatesDepends On
continuousMultilinearMapCompContinuousLinearMap 📖mathematicalDifferentiable
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.toAddCommGroup
SeminormedAddCommGroup.toIsTopologicalAddGroup
ContinuousMultilinearMap.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
ContinuousMultilinearMap.instTopologicalSpace
ContinuousLinearMap
RingHom.id
Semiring.toNonAssocSemiring
ContinuousLinearMap.addCommGroup
ContinuousLinearMap.module
ContinuousLinearMap.topologicalSpace
ContinuousMultilinearMap.compContinuousLinearMapSeminormedAddCommGroup.toIsTopologicalAddGroup
UniformContinuousConstSMul.to_continuousConstSMul
IsBoundedSMul.toUniformContinuousConstSMul
NormedSpace.toIsBoundedSMul
smulCommClass_self
DifferentiableAt.continuousMultilinearMapCompContinuousLinearMap

DifferentiableAt

Theorems

NameKindAssumesProvesValidatesDepends On
continuousMultilinearMapCompContinuousLinearMap 📖mathematicalDifferentiableAt
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.toAddCommGroup
SeminormedAddCommGroup.toIsTopologicalAddGroup
ContinuousMultilinearMap.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
ContinuousMultilinearMap.instTopologicalSpace
ContinuousLinearMap
RingHom.id
Semiring.toNonAssocSemiring
ContinuousLinearMap.addCommGroup
ContinuousLinearMap.module
ContinuousLinearMap.topologicalSpace
ContinuousMultilinearMap.compContinuousLinearMapSeminormedAddCommGroup.toIsTopologicalAddGroup
UniformContinuousConstSMul.to_continuousConstSMul
IsBoundedSMul.toUniformContinuousConstSMul
NormedSpace.toIsBoundedSMul
smulCommClass_self
nonempty_fintype
HasFDerivAt.differentiableAt
IsTopologicalAddGroup.toContinuousAdd
ContinuousMultilinearMap.instIsTopologicalAddGroup
RingHomCompTriple.ids
HasFDerivAt.continuousMultilinearMapCompContinuousLinearMap
hasFDerivAt

DifferentiableOn

Theorems

NameKindAssumesProvesValidatesDepends On
continuousMultilinearMapCompContinuousLinearMap 📖mathematicalDifferentiableOn
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.toAddCommGroup
SeminormedAddCommGroup.toIsTopologicalAddGroup
ContinuousMultilinearMap.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
ContinuousMultilinearMap.instTopologicalSpace
ContinuousLinearMap
RingHom.id
Semiring.toNonAssocSemiring
ContinuousLinearMap.addCommGroup
ContinuousLinearMap.module
ContinuousLinearMap.topologicalSpace
ContinuousMultilinearMap.compContinuousLinearMapSeminormedAddCommGroup.toIsTopologicalAddGroup
UniformContinuousConstSMul.to_continuousConstSMul
IsBoundedSMul.toUniformContinuousConstSMul
NormedSpace.toIsBoundedSMul
smulCommClass_self
DifferentiableWithinAt.continuousMultilinearMapCompContinuousLinearMap

DifferentiableWithinAt

Theorems

NameKindAssumesProvesValidatesDepends On
continuousMultilinearMapCompContinuousLinearMap 📖mathematicalDifferentiableWithinAt
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.toAddCommGroup
SeminormedAddCommGroup.toIsTopologicalAddGroup
ContinuousMultilinearMap.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
ContinuousMultilinearMap.instTopologicalSpace
ContinuousLinearMap
RingHom.id
Semiring.toNonAssocSemiring
ContinuousLinearMap.addCommGroup
ContinuousLinearMap.module
ContinuousLinearMap.topologicalSpace
ContinuousMultilinearMap.compContinuousLinearMapSeminormedAddCommGroup.toIsTopologicalAddGroup
UniformContinuousConstSMul.to_continuousConstSMul
IsBoundedSMul.toUniformContinuousConstSMul
NormedSpace.toIsBoundedSMul
smulCommClass_self
nonempty_fintype
HasFDerivWithinAt.differentiableWithinAt
IsTopologicalAddGroup.toContinuousAdd
ContinuousMultilinearMap.instIsTopologicalAddGroup
RingHomCompTriple.ids
HasFDerivWithinAt.continuousMultilinearMapCompContinuousLinearMap
hasFDerivWithinAt

HasFDerivAt

Theorems

NameKindAssumesProvesValidatesDepends On
continuousMultilinearMapCompContinuousLinearMap 📖mathematicalHasFDerivAt
SeminormedAddCommGroup.toAddCommGroup
NormedAddCommGroup.toSeminormedAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
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
NormedAddCommGroup.toAddCommGroup
SeminormedAddCommGroup.toIsTopologicalAddGroup
ContinuousMultilinearMap.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
ContinuousMultilinearMap.instTopologicalSpace
ContinuousLinearMap
RingHom.id
Semiring.toNonAssocSemiring
ContinuousLinearMap.addCommGroup
ContinuousLinearMap.module
ContinuousLinearMap.topologicalSpace
AddCommGroup.toAddCommMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
ContinuousMultilinearMap.compContinuousLinearMap
ContinuousMultilinearMap.addCommMonoid
ContinuousLinearMap.add
ContinuousMultilinearMap.normedAddCommGroup
ContinuousMultilinearMap.instIsTopologicalAddGroup
ContinuousLinearMap.comp
RingHomCompTriple.ids
ContinuousMultilinearMap.compContinuousLinearMapL
Pi.topologicalSpace
Pi.addCommMonoid
ContinuousLinearMap.addCommMonoid
Pi.module
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
ContinuousMultilinearMap.fderivCompContinuousLinearMap
ContinuousLinearMap.pi
SeminormedAddCommGroup.toIsTopologicalAddGroup
IsTopologicalAddGroup.toContinuousAdd
UniformContinuousConstSMul.to_continuousConstSMul
IsBoundedSMul.toUniformContinuousConstSMul
NormedSpace.toIsBoundedSMul
smulCommClass_self
ContinuousMultilinearMap.instIsTopologicalAddGroup
RingHomCompTriple.ids
RingHomIsometric.ids
comp
HasStrictFDerivAt.hasFDerivAt
ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap
prodMk
hasFDerivAt_pi
Finite.of_fintype

HasFDerivWithinAt

Theorems

NameKindAssumesProvesValidatesDepends On
continuousMultilinearMapCompContinuousLinearMap 📖mathematicalHasFDerivWithinAt
SeminormedAddCommGroup.toAddCommGroup
NormedAddCommGroup.toSeminormedAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
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
NormedAddCommGroup.toAddCommGroup
SeminormedAddCommGroup.toIsTopologicalAddGroup
ContinuousMultilinearMap.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
ContinuousMultilinearMap.instTopologicalSpace
ContinuousLinearMap
RingHom.id
Semiring.toNonAssocSemiring
ContinuousLinearMap.addCommGroup
ContinuousLinearMap.module
ContinuousLinearMap.topologicalSpace
AddCommGroup.toAddCommMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
ContinuousMultilinearMap.compContinuousLinearMap
ContinuousMultilinearMap.addCommMonoid
ContinuousLinearMap.add
ContinuousMultilinearMap.normedAddCommGroup
ContinuousMultilinearMap.instIsTopologicalAddGroup
ContinuousLinearMap.comp
RingHomCompTriple.ids
ContinuousMultilinearMap.compContinuousLinearMapL
Pi.topologicalSpace
Pi.addCommMonoid
ContinuousLinearMap.addCommMonoid
Pi.module
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
ContinuousMultilinearMap.fderivCompContinuousLinearMap
ContinuousLinearMap.pi
SeminormedAddCommGroup.toIsTopologicalAddGroup
IsTopologicalAddGroup.toContinuousAdd
UniformContinuousConstSMul.to_continuousConstSMul
IsBoundedSMul.toUniformContinuousConstSMul
NormedSpace.toIsBoundedSMul
smulCommClass_self
ContinuousMultilinearMap.instIsTopologicalAddGroup
RingHomCompTriple.ids
RingHomIsometric.ids
HasFDerivAt.comp_hasFDerivWithinAt
HasStrictFDerivAt.hasFDerivAt
ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap
prodMk
hasFDerivWithinAt_pi
Finite.of_fintype

HasStrictFDerivAt

Theorems

NameKindAssumesProvesValidatesDepends On
continuousMultilinearMapCompContinuousLinearMap 📖mathematicalHasStrictFDerivAt
SeminormedAddCommGroup.toAddCommGroup
NormedAddCommGroup.toSeminormedAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
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
NormedAddCommGroup.toAddCommGroup
SeminormedAddCommGroup.toIsTopologicalAddGroup
ContinuousMultilinearMap.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
ContinuousMultilinearMap.instTopologicalSpace
ContinuousLinearMap
RingHom.id
Semiring.toNonAssocSemiring
ContinuousLinearMap.addCommGroup
ContinuousLinearMap.module
ContinuousLinearMap.topologicalSpace
AddCommGroup.toAddCommMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
ContinuousMultilinearMap.compContinuousLinearMap
ContinuousMultilinearMap.addCommMonoid
ContinuousLinearMap.add
ContinuousMultilinearMap.normedAddCommGroup
ContinuousMultilinearMap.instIsTopologicalAddGroup
ContinuousLinearMap.comp
RingHomCompTriple.ids
ContinuousMultilinearMap.compContinuousLinearMapL
Pi.topologicalSpace
Pi.addCommMonoid
ContinuousLinearMap.addCommMonoid
Pi.module
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
ContinuousMultilinearMap.fderivCompContinuousLinearMap
ContinuousLinearMap.pi
SeminormedAddCommGroup.toIsTopologicalAddGroup
IsTopologicalAddGroup.toContinuousAdd
UniformContinuousConstSMul.to_continuousConstSMul
IsBoundedSMul.toUniformContinuousConstSMul
NormedSpace.toIsBoundedSMul
smulCommClass_self
comp
RingHomIsometric.ids
ContinuousMultilinearMap.instIsTopologicalAddGroup
RingHomCompTriple.ids
ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap
prodMk
hasStrictFDerivAt_pi
Finite.of_fintype

(root)

Definitions

NameCategoryTheorems
ContinuousMultilinearMap 📖CompData
720 mathmath: ContinuousMultilinearMap.map_piecewise_smul, fderiv_iteratedFDeriv, FormalMultilinearSeries.comp_rightInv_aux1, ContinuousMultilinearMap.norm_mkPiRing, FormalMultilinearSeries.comp_partialSum, AnalyticOn.exists_hasFTaylorSeriesUpToOn, FormalMultilinearSeries.removeZero_coeff_zero, ContinuousMultilinearMap.cpolynomialOn, FormalMultilinearSeries.ofScalars_apply_eq', ModularFormClass.qExpansionFormalMultilinearSeries_apply_norm, ContinuousMultilinearMap.map_smul_univ, FormalMultilinearSeries.ofScalars_eq_zero_of_scalar_zero, FormalMultilinearSeries.smul_apply, NormedSpace.expSeries_summable_of_mem_ball, ContinuousAlternatingMap.isClosedEmbedding_toContinuousMultilinearMap, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, ContinuousMultilinearMap.analyticAt_uncurry_compContinuousLinearMap, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm, hasFTaylorSeriesUpToOn_top_iff_right, HasFPowerSeriesWithinOnBall.hasSum_sub, ContinuousMultilinearMap.analyticAt_uncurry_of_linear, ContDiff.iteratedFDeriv_right, norm_iteratedFDerivWithin_smul_le, ContDiffMapSupportedIn.iteratedFDerivLM_apply, ContinuousMultilinearMap.norm_map_snoc_le, iteratedFDerivWithin_eventually_congr_set, ContinuousAlternatingMap.isUniformEmbedding_toContinuousMultilinearMap, ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars, FormalMultilinearSeries.changeOriginSeriesTerm_apply, norm_iteratedFDerivWithin_one, HasFTaylorSeriesUpTo.cont, ContinuousMultilinearMap.alternatization_apply_apply, ContinuousMultilinearMap.map_update_sub, FormalMultilinearSeries.congr, ContinuousMultilinearMap.coe_coe, norm_iteratedFDeriv_mul_le, AnalyticOnNhd.iteratedFDeriv_of_isOpen, ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries, ContDiffMapSupportedIn.structureMapCLM_apply, iteratedFDerivWithin_succ_eq_comp_right, iteratedDerivWithin_vcomp_two, HasFTaylorSeriesUpTo.hasFDerivAt, norm_iteratedFDerivWithin_clm_apply, ContinuousMultilinearMap.mkPiAlgebra_apply, bilinearIteratedFDerivTwo_eq_iteratedFDeriv, dist_iteratedFDerivWithin_one, FormalMultilinearSeries.norm_le_div_pow_of_pos_of_lt_radius, ContinuousLinearMap.norm_compContinuousMultilinearMap_le, FormalMultilinearSeries.le_changeOriginSeries_radius, MultilinearMap.mkContinuousMultilinear_apply, ContDiffPointwiseHolderAt.isBigO, SchwartzMap.decay', OrderedFinpartition.norm_compAlongOrderedFinpartition_le, ContinuousMultilinearMap.uniformContinuous_eval_const, OrderedFinpartition.norm_applyOrderedFinpartition_le, HasFPowerSeriesAt.eventually_hasSum, ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, ContinuousAlternatingMap.isClosed_range_toContinuousMultilinearMap, AnalyticOn.iteratedFDerivWithin, ContinuousMultilinearMap.toMultilinearMap_add, ContinuousMultilinearMap.contDiffAt, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear_of_le_one, FormalMultilinearSeries.changeOriginSeries_summable_aux₃, ContinuousMultilinearMap.piLinearEquiv_symm_apply, HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt, HasFDerivWithinAt.linear_multilinear_comp, iteratedFDerivWithin_succ_eq_comp_left, ContinuousMultilinearMap.opNorm_zero_iff, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_gt, contDiffOn_iff_continuousOn_differentiableOn, ContinuousMultilinearMap.mkPiRing_apply_one_eq_self, ContinuousMultilinearMap.mkPiRing_apply, norm_iteratedFDeriv_clm_apply, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, AnalyticOn.iteratedFDerivWithin_comp_perm, HasFTaylorSeriesUpToOn.zero_eq', FormalMultilinearSeries.ofScalars_apply_eq, HasFPowerSeriesWithinOnBall.isBigO_image_sub_image_sub_deriv_principal, HasFiniteFPowerSeriesAt.finite, FormalMultilinearSeries.id_apply_one', ContinuousMultilinearMap.norm_smulRightL_le, tensorIteratedFDerivTwo_eq_iteratedFDeriv, AnalyticOnNhd.iteratedFDeriv, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_eq_of_scalars, ContinuousMultilinearMap.norm_mkPiAlgebra_le, iteratedFDerivWithin_succ_const, formalMultilinearSeries_geometric_apply_norm_le, HasFPowerSeriesOnBall.hasSum_iteratedFDeriv, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform_aux, FormalMultilinearSeries.nnnorm_mul_pow_le_of_lt_radius, ContinuousMultilinearMap.curry0_apply, norm_iteratedFDerivWithin_zero, iteratedFDerivWithin_of_isOpen, ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear, HasFDerivAt.multilinear_comp, ContinuousMultilinearMap.linearDeriv_apply, NormedSpace.expSeries_apply_eq_div', Bornology.IsVonNBounded.image_multilinear', iteratedDerivWithin_eq_iteratedFDerivWithin, VectorFourier.fourierPowSMulRight_eq_comp, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, ContinuousLinearMap.flipMultilinear_apply_apply, ContinuousMultilinearMap.uncurrySum_apply, ContinuousMultilinearMap.map_sum, NormedSpace.expSeries_eq_expSeries, NormedSpace.expSeries_summable, FormalMultilinearSeries.comp_coeff_zero, FormalMultilinearSeries.ofScalars_eq_zero, FormalMultilinearSeries.ofScalars_apply_zero, ContinuousLinearMap.norm_iteratedFDerivWithin_comp_left, norm_iteratedFDerivWithin_clm_apply_const, ContinuousMultilinearMap.ext_ring_iff, FormalMultilinearSeries.nnnorm_changeOrigin_le, ContinuousMultilinearMap.isEmbedding_restrictScalars, InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_complexPlane, TrivSqZeroExt.fst_expSeries, ContinuousMultilinearMap.mkPiAlgebraFin_apply, FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum, ContinuousMultilinearMap.unit_le_opNorm, ContinuousMultilinearMap.curryRight_norm, ContDiffWithinAt.continuousWithinAt_iteratedFDerivWithin, ContinuousAlternatingMap.ofSubsingleton_apply_toContinuousMultilinearMap, iteratedFDeriv_add_apply, cauchyPowerSeries_apply, HasFPowerSeriesOnBall.coeff_zero, FormalMultilinearSeries.norm_apply_eq_norm_coef, ContDiffMapSupportedIn.seminorm_le_iff, ContinuousMultilinearMap.norm_compContinuous_linearIsometry_le, iteratedFDeriv_sum, tensorIteratedFDerivWithinTwo_eq_iteratedFDerivWithin, ContinuousMultilinearMap.opNorm_smul_le, ContinuousMultilinearMap.norm_restr, ContinuousMultilinearMap.norm_image_sub_le, iteratedFDerivWithin_const_smul_apply, HasFTaylorSeriesUpToOn.eventually_hasFDerivAt, NormedSpace.norm_expSeries_summable, MultilinearMap.coe_mkContinuous, ContinuousAlternatingMap.isEmbedding_toContinuousMultilinearMap, Function.hasTemperateGrowth_iff_isBigO, ContinuousMultilinearMap.map_update_add, iteratedFDerivWithin_neg_apply, ContinuousMultilinearMap.curryFinFinset_symm_apply_const, HasFPowerSeriesOnBall.fderiv_eq, ContinuousMultilinearMap.nnnorm_constOfIsEmpty, ContinuousMultilinearMap.neg_apply, PiTensorProduct.tprodL_toFun, iteratedFDerivWithin_succ_apply_right, HasFTaylorSeriesUpToOn.hasFDerivWithinAt, ContinuousMultilinearMap.curryLeft_norm, ContinuousMultilinearMap.uncurry0_norm, ContDiffOn.continuousOn_iteratedFDerivWithin, ContinuousMultilinearMap.le_opNorm, iteratedFDeriv_const_smul_apply, isBoundedBilinearMap_compMultilinear, norm_cauchyPowerSeries_le, ContDiffMapSupportedIn.structureMapLM_eq_of_scalars, iteratedFDeriv_succ_const, ContDiffAt.iteratedFDeriv_right, HasFPowerSeriesWithinAt.fderivWithin_eq, HasFTaylorSeriesUpToOn.cont, ContinuousMultilinearMap.norm_mkPiAlgebraFin_zero, NormedSpace.expSeries_hasSum_exp, ContinuousMultilinearMap.range_toUniformOnFun, FormalMultilinearSeries.hasSum, CPolynomialOn.iteratedFDeriv, FormalMultilinearSeries.coeff_eq_zero, ContinuousMultilinearMap.restrictScalarsLinear_apply, contDiffOn_nat_iff_continuousOn_differentiableOn, iteratedFDeriv_const_smul_apply', FormalMultilinearSeries.compAlongComposition_nnnorm, ContinuousLinearMap.compFormalMultilinearSeries_apply', LinearIsometry.norm_compContinuousMultilinearMap, ContDiff.differentiable_iteratedFDeriv, ContinuousMultilinearMap.isLeast_opNorm, ContinuousMultilinearMap.completeSpace, Quaternion.expSeries_odd_of_imaginary, HasFPowerSeriesWithinAt.coeff_zero, ContinuousMultilinearMap.cons_smul, ContDiffMapSupportedIn.uniformSpace_eq_iInf, PiTensorProduct.liftIsometry_tprodL, contDiffWithinAt_iff_of_ne_infty, ContinuousMultilinearMap.ofSubsingleton_symm_apply_apply, ContinuousMultilinearMap.hasFTaylorSeriesUpTo_iteratedFDeriv, VectorFourier.iteratedFDeriv_fourierIntegral, ContinuousMultilinearMap.map_piecewise_add, ContDiffMapSupportedIn.continuous_iff_comp_withOrder, ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear, ordinaryHypergeometricSeries_apply_eq', iteratedFDerivWithin_eq_equiv_comp, ContDiffMapSupportedIn.structureMapCLM_zero_apply, SchwartzMap.norm_iteratedFDeriv_le_seminorm, ContinuousMultilinearMap.prodEquiv_symm_apply_fst, ContinuousMultilinearMap.sum_apply, FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le, Bornology.IsVonNBounded.image_multilinear, ContDiffWithinAt.restrictScalars_iteratedFDerivWithin_eventuallyEq, ContinuousMultilinearMap.opNorm_nonneg, ContinuousMultilinearMap.hasBasis_nhds_zero, ContinuousMultilinearMap.instIsUniformAddGroup, Filter.EventuallyEq.iteratedFDerivWithin, compContinuousLinearMap_zero, ContinuousMultilinearMap.ofSubsingletonₗᵢ_symm_apply, FormalMultilinearSeries.apply_eq_pow_smul_coeff, continuousMultilinearCurryFin0_symm_apply, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply, FormalMultilinearSeries.compAlongComposition_bound, continuousMultilinearCurryRightEquiv_symm_apply, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le, ContinuousMultilinearMap.constOfIsEmpty_apply, hasFTaylorSeriesUpToOn_top_iff', ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply, ContinuousLinearMap.cpolyomialOn_uncurry_of_multilinear, ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall, OrderedFinpartition.compAlongOrderedFinpartitionₗ_apply_apply, PiTensorProduct.norm_eval_le_injectiveSeminorm, ContinuousLinearMap.fpowerSeriesBilinear_apply_add_three, contDiff_iff_continuous_differentiable, ContinuousAlternatingMap.toContinuousMultilinearMap_zero, ContinuousMultilinearMap.analyticAt, ContinuousMultilinearMap.prodL_apply, FormalMultilinearSeries.radius_inv_eq_limsup, hasFTaylorSeriesUpToOn_succ_iff_right, ContinuousLinearMap.coe_flipMultilinearEquiv, ContinuousMultilinearMap.norm_map_init_le, ordinaryHypergeometricSeries_apply_zero, NormedSpace.norm_expSeries_summable_of_mem_ball, binomialSeries_apply, iteratedFDeriv_neg_apply, PiTensorProduct.liftEquiv_symm_apply, ContinuousLinearMap.fpowerSeries_apply_add_two, ContinuousMultilinearMap.cons_add, ContinuousMultilinearMap.map_add_univ, FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum, ContinuousMultilinearMap.opNorm_zero, iteratedFDerivWithin_one_apply, FormalMultilinearSeries.ofScalars_norm_le, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le_of_pos, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, contDiffPointwiseHolderAt_iff, hasSum_cauchyPowerSeries_integral, HasFPowerSeriesWithinOnBall.hasSum_derivSeries_of_hasFDerivWithinAt, HasFPowerSeriesAt.isBigO_image_sub_norm_mul_norm_sub, LinearIsometry.norm_iteratedFDeriv_comp_left, ContDiffMapSupportedIn.structureMapLM_apply_withOrder, ContinuousMultilinearMap.coe_continuous, dist_iteratedFDerivWithin_zero, HasFPowerSeriesOnBall.hasSum, FormalMultilinearSeries.neg_apply, PiTensorProduct.liftEquiv_apply, hasFTaylorSeriesUpTo_top_iff', norm_iteratedFDerivWithin_prod_le, NormedSpace.expSeries_apply_eq, fderivWithin_iteratedFDerivWithin, ContinuousMultilinearMap.instContinuousEvalConstForall, ContinuousMultilinearMap.contDiff, MultilinearMap.mkContinuousLinear_norm_le, ContinuousMultilinearMap.piLinearEquiv_apply, FormalMultilinearSeries.not_summable_norm_of_radius_lt_nnnorm, FormalMultilinearSeries.norm_compContinuousLinearMap_le, ContinuousAlternatingMap.range_toContinuousMultilinearMap, ContinuousLinearMap.uncurryLeft_apply, HasFPowerSeriesWithinOnBall.image_sub_sub_deriv_le, ContinuousMultilinearMap.curryFinFinset_apply_const, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform, ContinuousMultilinearMap.compContinuousLinearMapLRight_apply, LinearIsometryEquiv.norm_iteratedFDerivWithin_comp_left, HasFPowerSeriesAt.hasStrictDerivAt, ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self, ContinuousMultilinearMap.apply_apply, ContinuousMultilinearMap.flipLinear_apply_apply, ContinuousAlternatingMap.norm_toContinuousMultilinearMap, ContinuousMultilinearMap.hasStrictFDerivAt, ContinuousMultilinearMap.pi_apply, hasFTaylorSeriesUpTo_succ_nat_iff_right, iteratedFDeriv_add, ContinuousMultilinearMap.isUniformEmbedding_toUniformOnFun, ContinuousMultilinearMap.toContinuousLinearMap_apply, ContinuousLinearMap.uncurryBilinear_apply, ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear, iteratedFDeriv_eq_equiv_comp, Quaternion.expSeries_even_of_imaginary, hasFTaylorSeriesUpToOn_succ_nat_iff_right, ContinuousMultilinearMap.uniformContinuous_restrictScalars, FormalMultilinearSeries.isLittleO_one_of_lt_radius, NormedSpace.expSeries_apply_eq_div, ContinuousAlternatingMap.toContinuousMultilinearMapLinear_apply, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_apply, ContinuousMultilinearMap.smul_prod_smul, HasFPowerSeriesAt.apply_eq_zero, ContinuousMultilinearMap.prodEquiv_symm_apply, FormalMultilinearSeries.comp_coeff_one, ContinuousMultilinearMap.opNorm_pi, iteratedDeriv_vcomp_three, iteratedFDerivWithin_two_apply', ContinuousMultilinearMap.instContinuousConstSMul, Filter.EventuallyEq.iteratedFDerivWithin', ContinuousLinearMap.continuousWithinAt_uncurry_of_multilinear, FormalMultilinearSeries.applyComposition_single, HasFPowerSeriesAt.fderiv_eq, continuousMultilinearCurryFin0_apply, PiTensorProduct.dualSeminorms_bounded, ContinuousMultilinearMap.curryMidEquiv_apply, ContinuousMultilinearMap.iteratedFDeriv_eq, FormalMultilinearSeries.le_mul_pow_of_radius_pos, HasFPowerSeriesOnBall.isBigO_image_sub_image_sub_deriv_principal, ContinuousMultilinearMap.instCompleteSpace, NormedSpace.expSeries_apply_zero, ContinuousOn.continuousOn_iteratedFDerivWithin, iteratedFDerivWithin_succ_apply_left, iteratedFDerivWithin_add_apply, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, ContinuousMultilinearMap.norm_mkPiAlgebra, ContinuousMultilinearMap.opNorm_add_le, ContinuousMultilinearMap.instContinuousEval, ContinuousMultilinearMap.norm_restrictScalars, ContinuousMultilinearMap.compContinuousLinearMap_apply, HasFTaylorSeriesUpToOn.fderivWithin, ContDiffAt.restrictScalars_iteratedFDeriv_eventuallyEq, ContinuousMultilinearMap.isLeast_opNNNorm, FormalMultilinearSeries.id_comp, ContinuousLinearMap.norm_map_tail_le, ContinuousMultilinearMap.map_coord_zero, ContinuousLinearMap.compContinuousMultilinearMap_coe, ContDiffAt.restrictScalars_iteratedFDeriv, PiTensorProduct.injectiveSeminorm_apply, norm_fderiv_iteratedFDeriv, ContinuousMultilinearMap.instIsBoundedSMul, ContinuousMultilinearMap.iteratedFDeriv_comp_diagonal, ContDiffMapSupportedIn.seminorm_le_iff_withOrder, InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_orthonormalBasis, iteratedDeriv_vcomp_eq_sum_orderedFinpartition, ordinaryHypergeometricSeries_apply_eq, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, HasFTaylorSeriesUpToOn.hasFDerivAt, HasFPowerSeriesAt.tendsto_partialSum_prod_of_comp, ContinuousMultilinearMap.uncurryRight_apply, LinearIsometry.norm_iteratedFDerivWithin_comp_left, iteratedDeriv_eq_equiv_comp, ContinuousMultilinearMap.cpolynomialAt, MultilinearMap.mkContinuousLinear_norm_le', norm_fderivWithin_iteratedFDerivWithin, HasFTaylorSeriesUpToOn.shift_of_succ, ContinuousMultilinearMap.prodEquiv_apply, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_symm, ContinuousMultilinearMap.ratio_le_opNorm, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap, iteratedFDeriv_zero_apply, ContinuousLinearMap.norm_iteratedFDeriv_comp_left, ContinuousLinearMap.norm_uncurryMid, ContinuousLinearMap.uncurryLeft_norm, MeasureTheory.AEStronglyMeasurable.fourierPowSMulRight, HasFDerivWithinAt.multilinear_comp, ContinuousMultilinearMap.add_apply, ContinuousMultilinearMap.prodEquiv_symm_apply_snd, FormalMultilinearSeries.compAlongComposition_norm, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral', ContDiff.continuous_iteratedFDeriv', formalMultilinearSeries_geometric_apply_norm, ContinuousLinearMap.continuous_uncurry_of_multilinear, constFormalMultilinearSeries_apply_of_nonzero, ContinuousMultilinearMap.instIsScalarTower, ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM, ContinuousMultilinearMap.piEquiv_apply, ContinuousMultilinearMap.isEmbedding_toUniformOnFun, MultilinearMap.mkContinuousMultilinear_norm_le', SchwartzMap.le_seminorm, ContinuousMultilinearMap.norm_ofSubsingleton_id_le, ContinuousMultilinearMap.curryRight_apply, ContDiff.fourierPowSMulRight, NormedSpace.expSeries_apply_eq', ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const, InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_stdOrthonormalBasis, AnalyticOn.iteratedFDeriv_comp_perm, ContinuousMultilinearMap.domDomCongr_apply, ContinuousMultilinearMap.toMultilinearMap_zero, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, ContinuousMultilinearMap.opNNNorm_prod, iteratedFDeriv_one_apply, ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft, HasFPowerSeriesOnBall.factorial_smul, iteratedFDeriv_succ_apply_right, FormalMultilinearSeries.leftInv_coeff_one, ContinuousAlternatingMap.uniformContinuous_toContinuousMultilinearMap, ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear, OrderedFinpartition.compAlongOrderedFinpartitionL_apply, HasFPowerSeriesAt.hasFDerivAt, FormalMultilinearSeries.comp_coeff_zero', ContinuousMultilinearMap.smul_apply, FormalMultilinearSeries.norm_mul_pow_le_mul_pow_of_lt_radius, LinearIsometryEquiv.norm_iteratedFDeriv_comp_right, HasFPowerSeriesOnBall.eventually_hasSum, IsSymmSndFDerivAt.iteratedFDeriv_cons, ContinuousMultilinearMap.instT3Space, ContDiffMapSupportedIn.iteratedFDeriv_zero_on_compl, FormalMultilinearSeries.id_apply_zero, PiTensorProduct.mapLMultilinear_apply_apply, ContinuousLinearMap.uncurryMid_apply, HasFPowerSeriesWithinOnBall.coeff_zero, ContinuousMultilinearMap.norm_iteratedFDeriv_le, ContinuousMultilinearMap.mkPiRing_zero, ContinuousMultilinearMap.norm_iteratedFDeriv_le', support_iteratedFDeriv_subset, InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis, ContinuousAlternatingMap.coe_mk, FormalMultilinearSeries.apply_eq_prod_smul_coeff, ContinuousMultilinearMap.toMultilinearMap_injective, ContinuousAlternatingMap.toContinuousMultilinearMap_injective, ContinuousMultilinearMap.le_opNorm_mul_pow_card_of_le, ContDiffMapSupportedIn.structureMapCLM_apply_withOrder, FormalMultilinearSeries.changeOriginSeries_summable_aux₁, PiTensorProduct.liftIsometry_comp_mapL, continuousMultilinearCurryLeftEquiv_apply, HasFPowerSeriesAt.deriv, HasCompactSupport.iteratedFDeriv, Set.EqOn.iteratedFDerivWithin, ContinuousMultilinearMap.alternatization_apply_toContinuousMultilinearMap, PiTensorProduct.liftIsometry_symm_apply, ContinuousMultilinearMap.iteratedFDerivComponent_apply, ContDiffWithinAt.differentiableWithinAt_iteratedFDerivWithin, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_withOrder, iteratedFDeriv_succ_eq_comp_right, SchwartzMap.iteratedPDeriv_eq_iteratedFDeriv, ContinuousMultilinearMap.changeOriginSeries_support, ContDiffMapSupportedIn.seminorm_apply, FormalMultilinearSeries.isLittleO_of_lt_radius, tsupport_iteratedFDeriv_subset, ContinuousMultilinearMap.hasFDerivAt, Real.iteratedFDeriv_fourier, ContinuousMultilinearMap.nnnorm_ofSubsingleton, ContinuousLinearMap.continuousOn_uncurry_of_multilinear, ContDiff.continuous_iteratedFDeriv, FormalMultilinearSeries.apply_eq_zero_of_lt_order, HasFPowerSeriesWithinAt.isBigO_image_sub_norm_mul_norm_sub, InnerProductSpace.laplacian_eq_iteratedFDeriv_complexPlane, bilinearIteratedFDerivWithinTwo_eq_iteratedFDeriv, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le, HasFPowerSeriesWithinOnBall.fderivWithin_eq, ContinuousMultilinearMap.piₗᵢ_symm_apply, ContDiff.iteratedFDeriv_right', MultilinearMap.mkContinuous_norm_le, HasFTaylorSeriesUpToOn.hasStrictFDerivAt, LinearIsometryEquiv.norm_iteratedFDerivWithin_comp_right, ContinuousMultilinearMap.hasBasis_nhds_zero_of_basis, ContinuousMultilinearMap.uniformContinuous_coe_fun, norm_iteratedFDeriv_prod_le, contDiff_nat_iff_continuous_differentiable, SchwartzMap.iteratedLineDerivOp_eq_iteratedFDeriv, OrderedFinpartition.compAlongOrderFinpartition_apply, ContDiffAt.iteratedFDeriv_comp_perm, ContinuousMultilinearMap.ofSubsingleton_apply_toMultilinearMap, ContinuousMultilinearMap.instUniformContinuousConstSMul, MultilinearMap.mkContinuousMultilinear_norm_le, HasFPowerSeriesAt.eventually_hasSum_of_comp, ContinuousMultilinearMap.opNNNorm_pi, ContinuousMultilinearMap.sub_apply, ContinuousMultilinearMap.coe_pi, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, ContinuousMultilinearMap.norm_domDomCongr, ContinuousMultilinearMap.curry0_norm, ContinuousAlternatingMap.nnnorm_toContinuousMultilinearMap, OrderedFinpartition.applyOrderedFinpartition_apply, HasFPowerSeriesOnBall.hasFDerivAt, ContinuousMultilinearMap.analyticOn, FormalMultilinearSeries.changeOriginSeries_summable_aux₂, ContinuousMultilinearMap.curryMid_apply, iteratedDeriv_eq_iteratedFDeriv, FormalMultilinearSeries.sub_apply, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, iteratedFDeriv_zero_fun, HasFPowerSeriesWithinOnBall.iteratedFDerivWithin_eq_sum_of_completeSpace, ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear, ContinuousMultilinearMap.map_update_smul, FormalMultilinearSeries.analyticAt_changeOrigin, PiTensorProduct.tprodL_apply, ContinuousMultilinearMap.instT2Space, HasFPowerSeriesAt.hasDerivAt, HasFPowerSeriesAt.eventually_hasSum_sub, ordinaryHypergeometricSeries_eq_zero_iff, HasFDerivAt.linear_multilinear_comp, FormalMultilinearSeries.compAlongComposition_apply, ContinuousMultilinearMap.le_opNorm_mul_prod_of_le, norm_iteratedFDeriv_one, iteratedFDerivWithin_eventually_congr_set', ContinuousMultilinearMap.analyticOnNhd, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_apply, ContinuousMultilinearMap.compContinuousLinearMapL_apply, HasFPowerSeriesWithinOnBall.iteratedFDerivWithin, PiTensorProduct.liftIsometry_apply_apply, ContinuousMultilinearMap.prodL_symm_apply, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, ContinuousMultilinearMap.alternatization_apply_toAlternatingMap, ContinuousMultilinearMap.instContinuousSMul, HasFPowerSeriesOnBall.eventually_hasSum_sub, ContinuousMultilinearMap.opNNNorm_le_iff, PiTensorProduct.norm_eval_le_projectiveSeminorm, iteratedFDeriv_zero_eq_comp, hasFTaylorSeriesUpToOn_succ_iff_left, ContinuousMultilinearMap.ofSubsingleton_apply_apply, ContDiffWithinAt.iteratedFDerivWithin_right, continuousMultilinearCurryRightEquiv_symm_apply', ContDiffMapSupportedIn.structureMapLM_zero_injective, iteratedDerivWithin_eq_equiv_comp, ContinuousMultilinearMap.nnnorm_ofSubsingleton_id_le, iteratedFDerivWithin_two_apply, ContinuousMultilinearMap.cpolynomialOn_uncurry_compContinuousLinearMap, ContinuousMultilinearMap.bound, ContinuousMultilinearMap.analyticWithinAt_uncurry_compContinuousLinearMap, ContinuousMultilinearMap.norm_mkPiAlgebraFin_succ_le, HasFiniteFPowerSeriesOnBall.finite, ContinuousMultilinearMap.instSMulCommClass, VectorFourier.fourierPowSMulRight_apply, NormedSpace.expSeries_eq_expSeries_rat, SchwartzMap.decay, ContinuousMultilinearMap.domDomCongrEquiv_apply, FormalMultilinearSeries.summable_nnnorm_mul_pow, ContinuousAlternatingMap.coe_toContinuousMultilinearMap, ContinuousMultilinearMap.map_sum_finset, ContinuousMultilinearMap.uncurry0_apply, OrderedFinpartition.norm_compAlongOrderedFinpartition_sub_compAlongOrderedFinpartition_le, ContinuousMultilinearMap.curryLeft_apply, ContinuousMultilinearMap.piEquiv_symm_apply, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_of_le_one, OrderedFinpartition.applyOrderedFinpartition_update_left, ContinuousMultilinearMap.norm_compContinuous_linearIsometryEquiv, iteratedFDerivWithin_zero_eq_comp, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral, ContinuousMultilinearMap.analyticWithinAt, ContinuousMultilinearMap.neg_prod_neg, InnerProductSpace.laplacian_eq_iteratedFDeriv_orthonormalBasis, Filter.EventuallyEq.iteratedFDeriv, ContinuousMultilinearMap.toUniformOnFun_toFun, ContinuousMultilinearMap.coe_restrictScalars, HasFPowerSeriesOnBall.iteratedFDeriv_eq_sum_of_completeSpace, Real.iteratedFDeriv_fourierIntegral, ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty, ContinuousLinearMap.analyticOn_uncurry_of_multilinear, FormalMultilinearSeries.order_eq_find', FormalMultilinearSeries.id_apply_of_one_lt, ContinuousMultilinearMap.nnnorm_ofSubsingleton_id, HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt, HasFPowerSeriesOnBall.image_sub_sub_deriv_le, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, Continuous.fourierPowSMulRight, iteratedFDerivWithin_sum_apply, ContinuousMultilinearMap.isUniformInducing_postcomp, ContinuousMultilinearMap.smulRight_apply, FormalMultilinearSeries.order_eq_find, iteratedFDerivWithin_clm_apply_const_apply, ContinuousMultilinearMap.currySum_apply, continuousMultilinearCurryRightEquiv_apply', ContinuousMultilinearMap.compAlongComposition_apply, ContDiffMapSupportedIn.bounded_iteratedFDeriv, HasFiniteFPowerSeriesOnBall.hasFDerivAt, ContDiffWithinAt.iteratedFDerivWithin_comp_perm, ContinuousMultilinearMap.domDomCongrEquiv_symm_apply, iteratedFDerivWithin_const_of_ne, ContinuousMultilinearMap.norm_ofSubsingleton, VectorFourier.norm_fourierPowSMulRight_le, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_apply, ContDiffMapSupportedIn.continuous_iff_comp, ContinuousMultilinearMap.norm_map_insertNth_le, HasFPowerSeriesAt.coeff_zero, SeparatingDual.completeSpace_continuousMultilinearMap_iff, norm_iteratedFDerivWithin_mul_le, HasFPowerSeriesOnBall.hasSum_sub, ContinuousMultilinearMap.instIsCentralScalar, FormalMultilinearSeries.radius_eq_top_iff_summable_norm, iteratedFDeriv_two_apply, ContinuousMultilinearMap.analyticOnNhd_uncurry_compContinuousLinearMap, iteratedDerivWithin_vcomp_eq_sum_orderedFinpartition, iteratedFDerivWithin_zero_fun, FormalMultilinearSeries.enorm_compContinuousLinearMap_le, continuousMultilinearCurryLeftEquiv_symm_apply, ContinuousMultilinearMap.smulRightL_apply, iteratedFDeriv_succ_eq_comp_left, ContinuousMultilinearMap.zero_apply, FormalMultilinearSeries.summable_norm_mul_pow, FormalMultilinearSeries.add_apply, ContDiffPointwiseHolderAt.iteratedFDeriv, FormalMultilinearSeries.applyComposition_update, ContDiffMapSupportedIn.structureMapCLM_zero_injective, ContinuousMultilinearMap.piₗᵢ_apply, ContinuousMultilinearMap.ext_iff, ContDiffAt.continuousAt_iteratedFDeriv, iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod, ContinuousMultilinearMap.ofSubsingletonₗᵢ_apply, norm_iteratedFDerivWithin_fderivWithin, continuousMultilinearCurryFin1_symm_apply, Quaternion.hasSum_expSeries_of_imaginary, ContinuousMultilinearMap.opNorm_le_iff, norm_iteratedFDeriv_smul_le, ContDiffAt.differentiableAt_iteratedFDeriv, iteratedDeriv_vcomp_two, ContinuousMultilinearMap.nnnorm_smulRight, ContinuousOn.continuousOn_iteratedFDeriv, ContinuousMultilinearMap.map_zero, ContinuousMultilinearMap.cpolynomialAt_uncurry_compContinuousLinearMap, ContinuousMultilinearMap.mkPiRing_eq_zero_iff, ContinuousMultilinearMap.norm_map_cons_le, ContinuousMultilinearMap.norm_smulRight, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_symm, ordinaryHypergeometricSeries_eq_zero_of_neg_nat, ContinuousMultilinearMap.continuousMapClass, FormalMultilinearSeries.derivSeries_apply_diag, iteratedFDeriv_clm_apply_const_apply, HasFPowerSeriesWithinOnBall.hasSum, FormalMultilinearSeries.norm_changeOriginSeriesTerm, ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply, ContinuousAlternatingMap.toContinuousMultilinearMap_smul, HasFTaylorSeriesUpTo.zero_eq', ContinuousMultilinearMap.norm_def, ContinuousAlternatingMap.toContinuousMultilinearMap_add, ContinuousMultilinearMap.curryFinFinset_symm_apply, FormalMultilinearSeries.id_apply_one, HasFTaylorSeriesUpTo.fderiv, ContinuousMultilinearMap.apply_zero_uncurry0, norm_iteratedFDeriv_zero, norm_iteratedFDeriv_eq_norm_iteratedDeriv, iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod, HasFiniteFPowerSeriesOnBall.fderiv_eq, FormalMultilinearSeries.zero_apply, FormalMultilinearSeries.summable, FormalMultilinearSeries.compContinuousLinearMap_apply, HasFPowerSeriesAt.hasStrictFDerivAt, isBoundedLinearMap_continuousMultilinearMap_comp_linear, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm, ContinuousMultilinearMap.sub_prod_sub, ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin, FormalMultilinearSeries.rightInv_coeff, ContinuousMultilinearMap.zero_prod_zero, FormalMultilinearSeries.summable_norm_apply, ContinuousMultilinearMap.norm_constOfIsEmpty, FormalMultilinearSeries.compAlongOrderedFinpartition_apply, ContDiffOn.differentiableOn_iteratedFDerivWithin, ContinuousMultilinearMap.le_opNorm_mul_pow_of_le, ContinuousMultilinearMap.le_opNNNorm, ContinuousMultilinearMap.norm_compContinuousLinearMapL_le, FormalMultilinearSeries.comp_rightInv_aux2, ContinuousMultilinearMap.opNorm_prod, FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm, continuousMultilinearCurryRightEquiv_apply, ContDiffMapSupportedIn.structureMapLM_zero_apply, ContinuousMultilinearMap.toMultilinearMap_smul, HasFPowerSeriesWithinAt.hasFDerivWithinAt, LinearIsometryEquiv.norm_iteratedFDeriv_comp_left, VectorFourier.integrable_fourierPowSMulRight, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, FormalMultilinearSeries.rightInv_coeff_one, HasFPowerSeriesWithinOnBall.iteratedFDerivWithin_eq_sum, ContinuousAlternatingMap.continuous_toContinuousMultilinearMap, ContinuousLinearMap.analyticAt_uncurry_of_multilinear, constFormalMultilinearSeries_apply_succ, ContinuousMultilinearMap.analyticOn_uncurry_compContinuousLinearMap, ContinuousAlternatingMap.enorm_toContinuousMultilinearMap, ContinuousMultilinearMap.isUniformInducing_toUniformOnFun, ContinuousLinearMap.fpowerSeries_apply_one, SchwartzMap.one_add_le_sup_seminorm_apply, ContinuousMultilinearMap.toMultilinearMapLinear_apply, ContinuousMultilinearMap.instIsTopologicalAddGroup, ContinuousMultilinearMap.norm_compContinuousLinearMap_le, ContinuousMultilinearMap.curryFinFinset_apply, OrderedFinpartition.applyOrderedFinpartition_update_right, MultilinearMap.mkContinuous_norm_le', SchwartzMap.integrable_pow_mul_iteratedFDeriv, FormalMultilinearSeries.radius_eq_liminf, ContinuousLinearMap.norm_map_removeNth_le, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, iteratedFDeriv_neg, ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, PiTensorProduct.mapLMultilinear_opNorm, ContinuousMultilinearMap.norm_image_sub_le', Function.HasTemperateGrowth.isBigO_uniform, iteratedFDerivWithin_zero_apply, FormalMultilinearSeries.norm_mul_pow_le_of_lt_radius, HasFPowerSeriesWithinOnBall.hasFDerivWithinAt, FormalMultilinearSeries.ofScalars_norm_eq_mul, NormedSpace.expSeries_hasSum_exp_of_mem_ball, ContDiffMapSupportedIn.structureMapLM_apply, isBoundedLinearMap_prod_multilinear, ContinuousMultilinearMap.prod_apply, FormalMultilinearSeries.applyComposition_ones, FormalMultilinearSeries.hasFPowerSeriesOnBall_changeOrigin, ContinuousMultilinearMap.fin0_apply_norm, ContinuousLinearMap.fpowerSeriesBilinear_apply_one, HasFPowerSeriesOnBall.iteratedFDeriv_eq_sum, TrivSqZeroExt.snd_expSeries_of_smul_comm, ContinuousMultilinearMap.norm_curryMid, ContinuousMultilinearMap.norm_mkPiAlgebraFin, ContinuousMultilinearMap.isUniformEmbedding_restrictScalars, ContinuousMultilinearMap.add_prod_add, iteratedFDerivWithin_add_apply', norm_iteratedFDeriv_fderiv, Function.HasTemperateGrowth.isBigO, ContinuousMultilinearMap.continuous_restrictScalars, ContinuousAlternatingMap.toMultilinearAddHom_apply, PiTensorProduct.injectiveSeminorm_def, ContDiffMapSupportedIn.structureMapLM_eq, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, IsSymmSndFDerivWithinAt.iteratedFDerivWithin_cons, FormalMultilinearSeries.ofScalars_norm, ContinuousMultilinearMap.norm_ofSubsingleton_id, ContinuousLinearMap.continuousAt_uncurry_of_multilinear, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_le, PiTensorProduct.mapLMultilinear_toFun_apply, iteratedDerivWithin_vcomp_three, ContinuousMultilinearMap.curryMidEquiv_symm_apply, FormalMultilinearSeries.comp_summable_nnreal, ContinuousMultilinearMap.uncurryRight_norm, AnalyticWithinAt.exists_hasFTaylorSeriesUpToOn, iteratedFDeriv_add_apply', iteratedFDeriv_succ_apply_left, iteratedFDeriv_const_of_ne, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux, continuousMultilinearCurryFin1_apply, norm_iteratedFDeriv_clm_apply_const

Theorems

NameKindAssumesProvesValidatesDepends On
fderivWithin_continuousMultilinearMapCompContinuousLinearMap 📖mathematicalDifferentiableWithinAt
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.toAddCommGroup
SeminormedAddCommGroup.toIsTopologicalAddGroup
ContinuousMultilinearMap.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
ContinuousMultilinearMap.instTopologicalSpace
ContinuousLinearMap
RingHom.id
Semiring.toNonAssocSemiring
ContinuousLinearMap.addCommGroup
ContinuousLinearMap.module
ContinuousLinearMap.topologicalSpace
UniqueDiffWithinAt
fderivWithin
ContinuousMultilinearMap.compContinuousLinearMap
AddCommGroup.toAddCommMonoid
ContinuousMultilinearMap.addCommMonoid
IsTopologicalAddGroup.toContinuousAdd
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
ContinuousLinearMap.add
NormedAddGroup.toAddGroup
NormedAddCommGroup.toNormedAddGroup
ContinuousMultilinearMap.normedAddCommGroup
ContinuousMultilinearMap.instIsTopologicalAddGroup
ContinuousLinearMap.comp
RingHomCompTriple.ids
ContinuousMultilinearMap.compContinuousLinearMapL
Pi.topologicalSpace
Pi.addCommMonoid
ContinuousLinearMap.addCommMonoid
Pi.module
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
ContinuousMultilinearMap.fderivCompContinuousLinearMap
ContinuousLinearMap.pi
SeminormedAddCommGroup.toIsTopologicalAddGroup
UniformContinuousConstSMul.to_continuousConstSMul
IsBoundedSMul.toUniformContinuousConstSMul
NormedSpace.toIsBoundedSMul
smulCommClass_self
HasFDerivWithinAt.fderivWithin
IsTopologicalAddGroup.toContinuousAdd
ContinuousMultilinearMap.instIsTopologicalAddGroup
RingHomCompTriple.ids
IsBoundedSMul.continuousSMul
ContinuousMultilinearMap.instContinuousSMul
ContinuousMultilinearMap.instT2Space
TopologicalSpace.t2Space_of_metrizableSpace
EMetricSpace.metrizableSpace
HasFDerivWithinAt.continuousMultilinearMapCompContinuousLinearMap
DifferentiableWithinAt.hasFDerivWithinAt
fderiv_continuousMultilinearMapCompContinuousLinearMap 📖mathematicalDifferentiableAt
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.toAddCommGroup
SeminormedAddCommGroup.toIsTopologicalAddGroup
ContinuousMultilinearMap.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
ContinuousMultilinearMap.instTopologicalSpace
ContinuousLinearMap
RingHom.id
Semiring.toNonAssocSemiring
ContinuousLinearMap.addCommGroup
ContinuousLinearMap.module
ContinuousLinearMap.topologicalSpace
fderiv
ContinuousMultilinearMap.compContinuousLinearMap
AddCommGroup.toAddCommMonoid
ContinuousMultilinearMap.addCommMonoid
IsTopologicalAddGroup.toContinuousAdd
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
ContinuousLinearMap.add
NormedAddGroup.toAddGroup
NormedAddCommGroup.toNormedAddGroup
ContinuousMultilinearMap.normedAddCommGroup
ContinuousMultilinearMap.instIsTopologicalAddGroup
ContinuousLinearMap.comp
RingHomCompTriple.ids
ContinuousMultilinearMap.compContinuousLinearMapL
Pi.topologicalSpace
Pi.addCommMonoid
ContinuousLinearMap.addCommMonoid
Pi.module
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
ContinuousMultilinearMap.fderivCompContinuousLinearMap
ContinuousLinearMap.pi
SeminormedAddCommGroup.toIsTopologicalAddGroup
UniformContinuousConstSMul.to_continuousConstSMul
IsBoundedSMul.toUniformContinuousConstSMul
NormedSpace.toIsBoundedSMul
smulCommClass_self
HasFDerivAt.fderiv
IsTopologicalAddGroup.toContinuousAdd
ContinuousMultilinearMap.instIsTopologicalAddGroup
RingHomCompTriple.ids
IsBoundedSMul.continuousSMul
ContinuousMultilinearMap.instContinuousSMul
ContinuousMultilinearMap.instT2Space
TopologicalSpace.t2Space_of_metrizableSpace
EMetricSpace.metrizableSpace
HasFDerivAt.continuousMultilinearMapCompContinuousLinearMap
DifferentiableAt.hasFDerivAt

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