Documentation Verification Report

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Definitionsstar, star, star, star, star, star, star, star, star, star, star, star, star
13
Theoremsstar, star, star, star, star, star, star, star, star, star, star, star, star, star, star, star, star, star, star, star, star, star, star, star, star, star, star, star, star, star, star, star, star, star
34
Total47

CategoryTheory.Functor

Definitions

NameCategoryTheorems
star 📖CompOp
16 mathmath: CategoryTheory.MorphismProperty.overEquivOfIsInitial_counitIso, CategoryTheory.underEquivOfIsTerminal_unitIso, CategoryTheory.underEquivOfIsTerminal_functor, star_obj_as, CategoryTheory.MorphismProperty.underEquivOfIsTerminal_counitIso, CategoryTheory.overEquivOfIsInitial_functor, CategoryTheory.MorphismProperty.underEquivOfIsTerminal_unitIso, FundamentalGroupoid.punitEquivDiscretePUnit_unitIso, CategoryTheory.MorphismProperty.underEquivOfIsTerminal_functor, CategoryTheory.underEquivOfIsTerminal_counitIso, CategoryTheory.overEquivOfIsInitial_unitIso, CategoryTheory.MorphismProperty.overEquivOfIsInitial_functor, CategoryTheory.overEquivOfIsInitial_counitIso, FundamentalGroupoid.punitEquivDiscretePUnit_counitIso, CategoryTheory.MorphismProperty.overEquivOfIsInitial_unitIso, FundamentalGroupoid.punitEquivDiscretePUnit_functor

CategoryTheory.MonoidalSingleObj

Definitions

NameCategoryTheorems
star 📖CompOp
8 mathmath: endMonoidalStarFunctorEquivalence_counitIso, endMonoidalStarFunctor_map, endMonoidalStarFunctor_isEquivalence, endMonoidalStarFunctor_obj, endMonoidalStarFunctorEquivalence_unitIso, endMonoidalStarFunctorEquivalence_inverse_map, endMonoidalStarFunctorEquivalence_functor, endMonoidalStarFunctorEquivalence_inverse_obj

CategoryTheory.Over

Definitions

NameCategoryTheorems
star 📖CompOp
10 mathmath: CategoryTheory.GrothendieckTopology.instIsContinuousOverStarOver, CategoryTheory.GrothendieckTopology.coverPreserving_over_star, forgetAdjStar_counit_app, starPullbackIsoStar_hom_app_left, instIsRightAdjointStar, star_obj_left, star_obj_hom, star_map_left, starPullbackIsoStar_inv_app_left, forgetAdjStar_unit_app_left

CategoryTheory.SingleObj

Definitions

NameCategoryTheorems
star 📖CompOp
13 mathmath: CategoryTheory.Limits.SingleObj.Types.sections.equivFixedPoints_apply_coe, CategoryTheory.Limits.SingleObj.Types.colimitEquivQuotient_symm_apply, CategoryTheory.Limits.SingleObj.Types.colimitEquivQuotient_apply, toEnd_def, CategoryTheory.Limits.SingleObj.Types.limitEquivFixedPoints_symm_apply, CategoryTheory.ActionCategory.π_obj, CategoryTheory.Limits.SingleObj.colimitTypeRelEquivOrbitRelQuotient_apply, Units.toAut_hom, CategoryTheory.Limits.SingleObj.colimitTypeRel_iff_orbitRel, CategoryTheory.Limits.SingleObj.Types.limitEquivFixedPoints_apply_coe, CategoryTheory.Limits.SingleObj.colimitTypeRelEquivOrbitRelQuotient_symm_apply, Units.toAut_inv, CategoryTheory.Limits.SingleObj.Types.sections.equivFixedPoints_symm_apply_coe

Continuous

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalContinuousContinuous
Star.star
comp
ContinuousStar.continuous_star

ContinuousAt

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalContinuousAtContinuousAt
Star.star
comp
continuousAt_star

ContinuousOn

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalContinuousOnContinuousOn
Star.star
Continuous.comp_continuousOn
ContinuousStar.continuous_star

ContinuousWithinAt

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalContinuousWithinAtContinuousWithinAt
Star.star
Filter.Tendsto.star

Differentiable

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalDifferentiable
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Differentiable
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
ESeminormedAddMonoid.toAddMonoid
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
DifferentiableAt.star

DifferentiableAt

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalDifferentiableAt
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
DifferentiableAt
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
ESeminormedAddMonoid.toAddMonoid
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
HasFDerivAt.differentiableAt
RingHomCompTriple.ids
RingHomInvPair.ids
HasFDerivAt.star
hasFDerivAt

DifferentiableOn

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalDifferentiableOn
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
DifferentiableOn
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
ESeminormedAddMonoid.toAddMonoid
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
DifferentiableWithinAt.star

DifferentiableWithinAt

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalDifferentiableWithinAt
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
DifferentiableWithinAt
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
ESeminormedAddMonoid.toAddMonoid
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
HasFDerivWithinAt.differentiableWithinAt
RingHomCompTriple.ids
RingHomInvPair.ids
HasFDerivWithinAt.star
hasFDerivWithinAt

Equiv

Definitions

NameCategoryTheorems
star 📖CompOp

Filter.EventuallyEq

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalFilter.EventuallyEqFilter.EventuallyEq
Star.star
Pi.instStarForall
fun_comp

Filter.Tendsto

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalFilter.Tendsto
nhds
Filter.Tendsto
Star.star
nhds
comp
Continuous.tendsto
ContinuousStar.continuous_star

HasDerivAt

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalHasDerivAt
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
IsBoundedSMul.continuousSMul
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
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
Module.toDistribMulAction
AddCommGroup.toAddCommMonoid
NormedSpace.toIsBoundedSMul
HasDerivAt
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
IsBoundedSMul.continuousSMul
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
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
Module.toDistribMulAction
AddCommGroup.toAddCommMonoid
NormedSpace.toIsBoundedSMul
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
ESeminormedAddMonoid.toAddMonoid
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
IsBoundedSMul.continuousSMul
NormedSpace.toIsBoundedSMul
HasDerivAtFilter.star

HasDerivAtFilter

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalHasDerivAtFilter
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
IsBoundedSMul.continuousSMul
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
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
Module.toDistribMulAction
AddCommGroup.toAddCommMonoid
NormedSpace.toIsBoundedSMul
HasDerivAtFilter
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
IsBoundedSMul.continuousSMul
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
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
Module.toDistribMulAction
AddCommGroup.toAddCommMonoid
NormedSpace.toIsBoundedSMul
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
ESeminormedAddMonoid.toAddMonoid
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
IsBoundedSMul.continuousSMul
NormedSpace.toIsBoundedSMul
RingHomCompTriple.ids
RingHomInvPair.ids
congr_simp
one_smul
HasFDerivAtFilter.hasDerivAtFilter
HasFDerivAtFilter.star
hasFDerivAtFilter

HasDerivWithinAt

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalHasDerivWithinAt
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
IsBoundedSMul.continuousSMul
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
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
Module.toDistribMulAction
AddCommGroup.toAddCommMonoid
NormedSpace.toIsBoundedSMul
HasDerivWithinAt
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
IsBoundedSMul.continuousSMul
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
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
Module.toDistribMulAction
AddCommGroup.toAddCommMonoid
NormedSpace.toIsBoundedSMul
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
ESeminormedAddMonoid.toAddMonoid
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
IsBoundedSMul.continuousSMul
NormedSpace.toIsBoundedSMul
HasDerivAtFilter.star

HasFDerivAt

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalHasFDerivAt
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
HasFDerivAt
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
ESeminormedAddMonoid.toAddMonoid
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
ContinuousLinearMap.comp
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
RingHom.id
Semiring.toNonAssocSemiring
AddCommGroup.toAddCommMonoid
ESeminormedAddCommMonoid.toAddCommMonoid
RingHomCompTriple.ids
ContinuousLinearEquiv.toContinuousLinearMap
CommSemiring.toSemiring
Semifield.toCommSemiring
RingHomInvPair.ids
starL'
HasFDerivAtFilter.star

HasFDerivAtFilter

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalHasFDerivAtFilter
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
HasFDerivAtFilter
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
ESeminormedAddMonoid.toAddMonoid
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
ContinuousLinearMap.comp
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
RingHom.id
Semiring.toNonAssocSemiring
AddCommGroup.toAddCommMonoid
ESeminormedAddCommMonoid.toAddCommMonoid
RingHomCompTriple.ids
ContinuousLinearEquiv.toContinuousLinearMap
CommSemiring.toSemiring
Semifield.toCommSemiring
RingHomInvPair.ids
starL'
comp
RingHomInvPair.ids
ContinuousLinearMap.hasFDerivAtFilter
Filter.tendsto_map

HasFDerivWithinAt

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalHasFDerivWithinAt
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
HasFDerivWithinAt
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
ESeminormedAddMonoid.toAddMonoid
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
ContinuousLinearMap.comp
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
RingHom.id
Semiring.toNonAssocSemiring
AddCommGroup.toAddCommMonoid
ESeminormedAddCommMonoid.toAddCommMonoid
RingHomCompTriple.ids
ContinuousLinearEquiv.toContinuousLinearMap
CommSemiring.toSemiring
Semifield.toCommSemiring
RingHomInvPair.ids
starL'
HasFDerivAtFilter.star

HasStrictDerivAt

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalHasStrictDerivAt
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
IsBoundedSMul.continuousSMul
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
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
Module.toDistribMulAction
AddCommGroup.toAddCommMonoid
NormedSpace.toIsBoundedSMul
HasStrictDerivAt
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
IsBoundedSMul.continuousSMul
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
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
Module.toDistribMulAction
AddCommGroup.toAddCommMonoid
NormedSpace.toIsBoundedSMul
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
ESeminormedAddMonoid.toAddMonoid
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
IsBoundedSMul.continuousSMul
NormedSpace.toIsBoundedSMul
HasDerivAtFilter.star

HasStrictFDerivAt

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalHasStrictFDerivAt
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
HasStrictFDerivAt
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
ESeminormedAddMonoid.toAddMonoid
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
ContinuousLinearMap.comp
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
RingHom.id
Semiring.toNonAssocSemiring
AddCommGroup.toAddCommMonoid
ESeminormedAddCommMonoid.toAddCommMonoid
RingHomCompTriple.ids
ContinuousLinearEquiv.toContinuousLinearMap
CommSemiring.toSemiring
Semifield.toCommSemiring
RingHomInvPair.ids
starL'
HasFDerivAtFilter.star

HasSum

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalHasSumHasSum
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
map
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
ContinuousStar.continuous_star

Invertible

Definitions

NameCategoryTheorems
star 📖CompOp

IsIdempotentElem

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalIsIdempotentElemIsIdempotentElem
Star.star
InvolutiveStar.toStar
StarMul.toInvolutiveStar
star_iff

IsLeftRegular

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalIsLeftRegularIsRightRegular
Star.star
InvolutiveStar.toStar
StarMul.toInvolutiveStar
star_injective
StarMul.star_mul
star_star

IsRegular

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalIsRegularIsRegular
Star.star
InvolutiveStar.toStar
StarMul.toInvolutiveStar
IsRightRegular.star
right
IsLeftRegular.star
left

IsRightRegular

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalIsRightRegularIsLeftRegular
Star.star
InvolutiveStar.toStar
StarMul.toInvolutiveStar
star_injective
StarMul.star_mul
star_star

IsStarNormal

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalIsStarNormal
InvolutiveStar.toStar
StarMul.toInvolutiveStar
Star.star
star_star
star_comm_self'

IsUnit

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalIsUnitIsUnit
Star.star
InvolutiveStar.toStar
StarMul.toInvolutiveStar
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass

Lean.Meta.RefinedDiscrTree.Trie

Definitions

NameCategoryTheorems
star 📖CompOp

Mathlib.Tactic.ExtractGoal

Definitions

NameCategoryTheorems
star 📖CompOp

MeasureTheory.AEStronglyMeasurable

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalMeasureTheory.AEStronglyMeasurableMeasureTheory.AEStronglyMeasurable
Star.star
Pi.instStarForall
MeasureTheory.Measure.instOuterMeasureClass
MeasureTheory.StronglyMeasurable.star
Filter.EventuallyEq.star

MeasureTheory.MemLp

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalMeasureTheory.MemLp
ContinuousENorm.toENorm
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddGroup.toPseudoMetricSpace
SeminormedAddCommGroup.toSeminormedAddGroup
NormedAddCommGroup.toSeminormedAddCommGroup
SeminormedAddGroup.toContinuousENorm
SeminormedAddCommGroup.toPseudoMetricSpace
MeasureTheory.MemLp
ContinuousENorm.toENorm
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddGroup.toPseudoMetricSpace
SeminormedAddCommGroup.toSeminormedAddGroup
NormedAddCommGroup.toSeminormedAddCommGroup
SeminormedAddGroup.toContinuousENorm
SeminormedAddCommGroup.toPseudoMetricSpace
Star.star
Pi.instStarForall
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
ESeminormedAddMonoid.toAddMonoid
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
MeasureTheory.AEStronglyMeasurable.star
NormedStarGroup.to_continuousStar
MeasureTheory.eLpNorm_star

MeasureTheory.StronglyMeasurable

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalMeasureTheory.StronglyMeasurableMeasureTheory.StronglyMeasurable
Star.star
Pi.instStarForall
Filter.Tendsto.star
tendsto_approx

Prefunctor

Definitions

NameCategoryTheorems
star 📖CompOp
9 mathmath: IsCovering.star_bijective, star_fst, costar_conj_star, symmetrifyStar, star_apply, symmetrifyCostar, star_comp, star_snd, bijective_costar_iff_bijective_star

Quiver.SingleObj

Definitions

NameCategoryTheorems
star 📖CompOp
9 mathmath: pathEquivList_nil, pathEquivList_symm_cons, toHom_apply, pathToList_listToPath, toHom_symm_apply, pathEquivList_symm_nil, pathEquivList_cons, toPrefunctor_symm_apply, listToPath_pathToList

RingQuot.Rel

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalStar.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
StarRing.toStarAddMonoid
RingQuot.Rel
RingQuot.Rel
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
StarRing.toStarAddMonoid
StarAddMonoid.star_add
StarMul.star_mul

Set

Definitions

NameCategoryTheorems
star 📖CompOp
31 mathmath: image_star, star_mem_centralizer, Subalgebra.star_adjoin_comm, nonempty_star, star_inv', star_add, NonUnitalStarAlgebra.adjoin_toNonUnitalSubalgebra, star_inv, NonUnitalStarAlgebra.adjoin_eq_span, instTrivialStar, iUnion_star, union_star, Subalgebra.coe_star, star_univ, NonUnitalStarAlgebra.star_subset_adjoin, compl_star, NonUnitalSubalgebra.coe_star, Finite.star, spectrum.map_star, inter_star, Nonempty.star, star_subset, star_singleton, mem_star, star_mem_star, star_subset_star, iInter_star, star_empty, star_mul, star_preimage, NonUnitalSubalgebra.star_adjoin_comm

Set.Finite

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalSet.Finite
Star.star
Set
Set.star
InvolutiveStar.toStar
preimage
Function.Injective.injOn
star_injective

Set.Nonempty

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalSet.NonemptySet.Nonempty
Star.star
Set
Set.star
InvolutiveStar.toStar
Set.nonempty_star

Star

Definitions

NameCategoryTheorems
star 📖CompOp
696 mathmath: unitary.spectrum.unitary_conjugate, ContinuousMapZero.coe_star, NonUnitalSubalgebra.coe_starClosure, Quaternion.star_mul_self, Quaternion.coe_normSq_add, unitary.star_eq_inv', star_eq_zero, Quaternion.re_star, star_mul_star, QuaternionAlgebra.self_add_star, IsIdempotentElem.star_iff, Matrix.star_eq_conjTranspose, DoubleCentralizer.star_snd, differentiableOn_star_iff, norm_star, IsUnit.star, Set.image_star, star_comm_self', star_ofNat, spinGroup.star_eq_inv, Quaternion.star_smul, IsUnit.isStrictlyPositive_star_right_conjugate_iff, RingHom.star_apply, IsSelfAdjoint.star_mul_self, spinGroup.coe_star_mul_self, Unitary.conjStarAlgAut_symm, RCLike.star_def, Quaternion.star_eq_neg, BoundedContinuousFunction.mkOfCompact_star, pinGroup.coe_star_mul_self, CentroidHom.star_centerToCentroidCenter, QuaternionAlgebra.star_eq_two_re_sub, isRightRegular_star_iff, BoundedContinuousFunction.char_neg, val_inv_unitarySubgroupUnitsEquiv_symm_apply_coe, TensorProduct.star_tmul, CliffordAlgebraQuaternion.toQuaternion_star, lp.coeFn_star, Set.star_mem_centralizer, unitary.inv_mul_mem_iff, NumberField.mem_maximalRealSubfield_iff, Complex.star_def, Matrix.isHermitian_comp_iff_forall, Subalgebra.star_adjoin_comm, LinearMap.intrinsicStar_mulRight, LE.le.star_eq, Module.End.spectrum_intrinsicStar, IsUnit.star_right_conjugate_nonneg_iff, ContinuousLinearMap.intrinsicStar_toSpanSingleton, cfc_comp_star, IsCHSHTuple.B₀_sa, spinGroup.star_eq_inv', QuaternionAlgebra.mul_star_eq_coe, commute_star_star, hasDerivAt_star_conj_iff, CFC.abs_nnrpow_two, summable_star_iff, Pi.star_mulSingle, Matrix.intrinsicStar_toLin', dotProduct_star_self_eq_zero, Matrix.posDef_iff_dotProduct_mulVec, Matrix.IsHermitian.eigenvalues_eq, LinearMap.intrinsicStar_toSpanSingleton, pinGroup.star_mul_self, ContinuousStar.continuous_star, star_dotProduct_toMatrix₂_mulVec, Complex.UnitDisc.conj_neg, Set.nonempty_star, WithCStarModule.inner_def, Matrix.star_vec, unitary.coe_star_mul_self, deriv.star, ContinuousLinearMap.IntrinsicStar.isSelfAdjoint_iff_map_star, star_star, MulOpposite.op_star, Pi.star_single, Unitary.inv_mul_mem_iff, Matrix.IsUnit.posSemidef_star_right_conjugate_iff, IsCHSHTuple.B₁_sa, Pell.pellZd_sub, Set.star_centralizer, HasStrictFDerivAt.star, Memℓp.star_mem, Set.star_inv', unitary.spectrum.unitary_conjugate', unitary.mem_iff_self_mul_star, Complex.UnitDisc.im_star, HasFDerivAt.star, unitary.star_mul_self_of_mem, continuousOn_star, StarOrderedRing.lt_iff, smul_mem_closure_star_mul, CStarRing.norm_mul_self_le, Matrix.IsHermitian.apply, skewAdjoint.mem_iff, CompactlySupportedContinuousMap.star_apply, InvolutiveStar.star_involutive, Matrix.dotProduct_star_self_pos_iff, Unitization.inr_star, fderivWithin_star, IsStarNormal.star_comm_self, IsSelfAdjoint.add_star_self, IsSelfAdjoint.mul_star_self, MulChar.star_apply, Matrix.conjTranspose_eq_diagonal, Matrix.posSemidef_vecMulVec_self_star, QuaternionAlgebra.star_mul_eq_coe, Module.End.mem_eigenspace_intrinsicStar_iff, Matrix.star_dotProduct, IsLeftRegular.star, starMulAut_apply, StarOrderedRing.pos_iff, QuaternionAlgebra.star_im, Zsqrtd.im_star, StarAddMonoid.star_add, Pi.single_star, PositiveLinearMap.preGNS_norm_def, star_pos_iff, spinGroup.coe_mul_star_self, Quaternion.inv_def, eq_star_of_eq_star, CliffordAlgebra.star_def', starL_apply, StarModule.star_smul, QuaternionAlgebra.star_coe, FreeAlgebra.star_algebraMap, Pi.intrinsicStar_comul_commSemiring, CStarMatrix.conjTranspose_apply, CompactlySupportedContinuousMap.coe_star, Pell.isPell_norm, Unitary.spectrum_star_left_conjugate, MeasureTheory.MemLp.star, spinGroup.mul_star_self_of_mem, Set.star_add, Complex.UnitDisc.coe_conj, Units.mul_inv_mem_unitary, starRingAut_apply, DifferentiableAt.star_conj, Matrix.dotProduct_star, star_zsmul, eq_star_iff_eq_star, unitary.mem_iff, NonUnitalStarAlgebra.adjoin_toNonUnitalSubalgebra, Matrix.IsHermitian.ext_iff, Unitary.mem_iff_self_mul_star, Matrix.mem_unitaryGroup_iff, HasFDerivWithinAt.star, Matrix.star_dotProduct_star, star_right_conjugate_pos, CFC.abs_nnrpow, Matrix.star_vec_dotProduct_vec, MeasureTheory.AEStronglyMeasurable.star, CliffordAlgebra.star_def, Quaternion.nnnorm_star, nnnorm_star, MeasureTheory.SimpleFunc.coe_star, CFC.norm_star_mul_mul_self_of_nonneg, isStarNormal_iff, Complex.UnitDisc.conj_mul, Filter.EventuallyEq.fun_star, LinearMap.intrinsicStar_mul', differentiableAt_star_iff, NumberField.ComplexEmbedding.IsConj.eq, mul_star_self_nonneg, star_left_conjugate_pos, CentroidHom.star_apply, ContinuousLinearMap.intrinsicStar_comp, Quaternion.star_eq_two_re_sub, Unitary.expUnitary_eq_mul_inv, QuaternionAlgebra.star_smul', Matrix.star_vecMul, CStarModule.inner_smul_left_complex, Unitary.star_mul_self_of_mem, HasDerivAt.star, Quaternion.star_add_self, star_isometry, unitary.norm_sub_eq, StarRing.star_add, CStarModule.star_inner, RingQuot.Rel.star, unitary.mem_iff_star_mul_self, Pi.intrinsicStar_comul, Zsqrtd.norm_conj, CStarRing.norm_star_mul_self', Units.coe_star, Matrix.Fin.conjTranspose_circulant, RCLike.mul_wInner_left, StarMemClass.star_coe_eq, Matrix.star_apply, IsCHSHTuple.A₁_sa, PositiveLinearMap.preGNS_inner_def, differentiableAt_star_conj_iff, star_natCast_smul, starL'_apply, Unitary.coe_mul_star_self, star_intCast, LinearMap.intrinsicStar_zero, Matrix.det_conjTranspose, tendsto_star, NonUnitalSubalgebra.mem_star_iff, Unitary.mul_star_self, Unitary.spectrum_star_right_conjugate, gelfandTransform_map_star, dotProduct_star_self_nonneg, Matrix.map_star_mem_unitaryGroup_iff, FreeMonoid.star_one, StarMemClass.star_mem, pinGroup.star_mem, star_neg, FreeAlgebra.star_ι, star_ratCast_smul, Subalgebra.mem_starClosure, star_finsuppProd, MulOpposite.unop_star, QuadraticAlgebra.star_mem_nonZeroDivisors_iff, Set.star_inv, CStarRing.star_mul_self_eq_zero_iff, selfAdjoint.star_val_eq, QuadraticAlgebra.star_mk, StarHomClass.map_star, Unitization.inl_star, star_mul_self_eq_realPart_sq_add_imaginaryPart_sq, NonUnitalStarSubsemiring.star_mem', Zsqrtd.star_mk, QuaternionAlgebra.star_eq_self, star_nnrat_smul, TrivialStar.star_trivial, MeasureTheory.eLpNorm_star, NonUnitalStarAlgebra.adjoin_eq_span, ContinuousLinearMap.toLinearMap_intrinsicStar, CliffordAlgebraQuaternion.ofQuaternion_star, Matrix.conjTranspose_replicateRow, LinearMap.IntrinsicStar.isSelfAdjoint_iff_map_star, LinearMap.intrinsicStar_comp', Matrix.schur_complement_eq₂₂, DoubleCentralizer.star_fst, NormedStarGroup.norm_star_le, QuaternionAlgebra.star_add_self, CStarMatrix.star_apply, QuadraticAlgebra.mul_star, Matrix.transpose_conjTranspose, LinearMap.intrinsicStar_rTensor, LinearMap.toMatrix_innerₛₗ_apply, star_lt_one_iff, star_inv_intCast_smul, CFC.abs_nnrpow_two_mul, Matrix.PosSemidef.toLinearMap₂'_zero_iff, NormedSpace.star_exp, TensorProduct.intrinsicStar_map, unitary.star_mem, CliffordAlgebra.star_smul, pinGroup.star_eq_inv', Set.iUnion_star, CStarAlgebra.isStrictlyPositive_iff_eq_mul_star_self, HasDerivAtFilter.star, CFC.abs_star, IsUnit.isStrictlyPositive_star_left_conjugate_iff, NonUnitalStarSubalgebra.coe_centralizer, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, star_mul_self_add_self_mul_star, differentiableWithinAt_star_iff, star_sum, StarSubalgebra.centralizer_toSubalgebra, Filter.EventuallyEq.star, Set.union_star, IsCHSHTuple.A₀_sa, GaussianInt.toComplex_star, Circle.star_addChar, StarSubalgebra.star_mem', Ring.inverse_star, starRingEnd_apply, StarAlgebra.star_self_mem_adjoin_singleton, Unitary.star_mul_self, LinearMap.star_eq_adjoint, IsUnit.star_left_conjugate_nonneg_iff, Complex.UnitDisc.im_conj, Matrix.UnitaryGroup.inv_val, NonUnitalStarSubalgebra.mem_centralizer_iff, QuaternionAlgebra.star_add_self', Unitary.mul_inv_mem_iff, GaussianInt.div_def, isRegular_star_iff, Summable.star, Function.star_sumElim, QuadraticAlgebra.coe_norm_eq_mul_star, StarAlgebra.star_subset_adjoin, starMulEquiv_apply, star_mul_self_nonneg, QuaternionAlgebra.imK_star, Matrix.star_mul, IsUnit.isSelfAdjoint_conjugate_iff, ContinuousLinearMap.intrinsicStar_zero, star_nsmul, Unitary.conjStarAlgAut_apply, Quaternion.mul_star_eq_coe, QuadraticAlgebra.re_star, starₗᵢ_apply, isStarProjection_iff', RCLike.wInner_smul_left, Unitary.mem_iff_star_mul_self, star_right_conjugate_lt_conjugate, Subalgebra.coe_star, apply_eq_star_dotProduct_toMatrix₂_mulVec, Quaternion.normSq_add, mul_star_self_pos, ContinuousLinearMap.intrinsicStar_eq_comp, LinearMap.toMatrix'_intrinsicStar, Set.star_univ, Matrix.trace_conjTranspose, Quaternion.imI_star, Matrix.diagonal_conjTranspose, star_injective, imaginaryPart_apply_coe, Matrix.posSemidef_vecMulVec_star_self, Quaternion.imK_star, NonUnitalStarAlgebra.star_subset_adjoin, StarMulEquiv.map_star', CStarRing.norm_star_mul_self, spinGroup.mul_star_self, unitary.coe_mul_star_self, Zsqrtd.norm_eq_mul_conj, Quaternion.star_add_self', Subalgebra.starClosure_toSubalgebra, CStarModule.inner_op_smul_left, CStarMatrix.mul_entry_mul_eq_inner_toCLM, Set.compl_star, QuaternionAlgebra.coe_starAe, one_lt_star_iff, star_inv_natCast_smul, StarAlgebra.elemental.star_self_mem, star_lt_star_iff, HasFDerivAtFilter.star, IsSelfAdjoint.star_iff, Matrix.schur_complement_eq₁₁, EuclideanSpace.inner_eq_star_dotProduct, NonUnitalSubalgebra.coe_star, QuaternionAlgebra.self_add_star', star_qsmul, cfc_star_id, Unitary.symm_mulRight, Unitary.conjStarAlgAut_symm_apply, spectrum.star_mem_resolventSet_iff, selfAdjoint.star_coe_unitarySelfAddISMul, Prod.star_def, Quaternion.self_add_star', StarMemClass.coe_star, star_nnqsmul, skewAdjoint.star_val_eq, Set.Finite.star, CStarAlgebra.mul_star_le_algebraMap_norm_sq, pinGroup.mul_star_self, Quaternion.star_im, Pi.star_apply, spectrum.map_star, StarRingEquiv.map_star', Memℓp.star_iff, star_right_conjugate_le_conjugate, star_le_iff, star_eq_iff_star_eq, star_prod, MulChar.star_apply', NonUnitalStarAlgebra.elemental.star_self_mem, Set.inter_star, IsRightRegular.star, pinGroup.star_mem_iff, star_lt_iff, CFC.abs_mul_self, conjugate_lt_conjugate', ContinuousMap.star_apply, HasSum.star, isLeftRegular_star_iff, star_nnratCast, Zsqrtd.re_star, dotProduct_self_star_nonneg, LinearMap.intrinsicStar_convMul, conjugate_lt_conjugate, Complex.UnitDisc.re_star, Set.star_mem_center, spinGroup.star_mem, LinearMap.intrinsicStar_id, InnerProductSpace.toMatrix_rankOne, CliffordAlgebra.star_ι, Unitary.coe_map_star, Matrix.PosSemidef.dotProduct_mulVec_nonneg, CStarRing.norm_self_mul_star, skewAdjointPart_apply_coe, CStarAlgebra.conjugate_le_norm_smul', StarSubsemiring.star_mem', Matrix.star_eq_inv, selfAdjointPartL_apply_coe, Quaternion.self_mul_star, Matrix.mulVec_conjTranspose, StarRingEquivClass.map_star, QuadraticAlgebra.star_mem_nonZeroDivisors, ContinuousLinearMap.intrinsicStar_smulRight, LinearMap.intrinsicStar_mulLeft, one_le_star_iff, CStarAlgebra.star_mul_le_algebraMap_norm_sq, SemiconjBy.star_star_star, Quaternion.inner_def, Zsqrtd.mul_star, Matrix.posSemidef_iff_eq_sum_vecMulVec, Matrix.vecMul_conjTranspose, StarAlgebra.adjoin_toSubalgebra, LinearMap.intrinsicStar_lTensor, QuaternionAlgebra.im_star, unitary.coe_map_star, Set.Nonempty.star, conjugate_pos', star_zero, NonUnitalSubalgebra.star_mono, Pi.star_def, CStarAlgebra.star_left_conjugate_le_norm_smul, StarOrderedRing.le_iff, ContinuousWithinAt.star, MeasureTheory.AEEqFun.coeFn_star, Quaternion.im_star, coe_starₗᵢ, Set.star_subset, Matrix.star_dotProduct_gram_mulVec, MulChar.star_eq_inv, Subalgebra.topologicalClosure_star_comm, StarSubalgebra.coe_centralizer_centralizer, Pell.isPell_star, isSelfAdjoint_conjugate_iff_of_isUnit', Subalgebra.star_mem_star_iff, Quaternion.coe_starAe, toMatrix_innerSL_apply, LinearMap.intrinsicStar_single, Matrix.PosSemidef.re_dotProduct_nonneg, IsStarNormal.star, LinearMap.intrinsicStar_smulRight, star_id_of_comm, star_left_conjugate_le_conjugate, NonUnitalStarSubalgebra.coe_centralizer_centralizer, Filter.IsIncreasingApproximateUnit.eventually_star_eq, Matrix.posSemidef_iff_dotProduct_mulVec, CStarAlgebra.nonneg_iff_eq_star_mul_self, pinGroup.star_mul_self_of_mem, DifferentiableAt.star_star, Filter.Tendsto.star, NonUnitalStarSubalgebra.centralizer_toNonUnitalSubalgebra, Quaternion.self_add_star, Quaternion.normSq_def, ContinuousLinearMap.intrinsicStar_comp', skewAdjoint.conjugate', StarOrderedRing.nonneg_iff, cfc_unitary_iff, ContinuousLinearMap.intrinsicStar_id, Matrix.conjTranspose_apply, Matrix.PosSemidef.dotProduct_mulVec_zero_iff, HasDerivWithinAt.star, CliffordAlgebra.star_algebraMap, BoundedContinuousFunction.star_mem_range_charAlgHom, cfcₙ_norm_sq_nonneg, Function.update_star, StarSubalgebra.mem_centralizer_iff, selfAdjointPart_apply_coe, skewAdjointPartL_apply_coe, BoundedContinuousFunction.star_apply, star_div, RingHom.star_def, ContinuousMap.coe_star, Quaternion.star_mul_eq_coe, IsSelfAdjoint.star_add_self, star_left_conjugate_lt_conjugate, Matrix.isSymm_iff_intrinsicStar_toLin', Matrix.specialUnitaryGroup.coe_star, Complex.UnitDisc.re_conj, Complex.UnitDisc.conj_conj, conjugate_nonneg', BoundedContinuousFunction.coe_star, Unitary.norm_sub_eq, CStarAlgebra.nonneg_iff_eq_mul_star_self, pinGroup.star_eq_inv, QuaternionAlgebra.imJ_star, CStarAlgebra.conjugate_le_norm_smul, unitary.coe_star, CStarAlgebra.isStrictlyPositive_iff_eq_star_mul_self, ContinuousOn.star, Matrix.mem_unitaryGroup_iff', Set.star_singleton, Unitary.mul_star_self_of_mem, NonUnitalStarSubalgebra.star_mem', selfAdjoint.mem_iff, Matrix.updateCol_conjTranspose, unitary.mul_inv_mem_iff, CFC.abs_sq, LinearMap.intrinsicStar_apply, Subalgebra.coe_starClosure, Unitization.snd_star, FreeMonoid.star_of, DifferentiableAt.star, LinearMap.isSelfAdjoint_iff_map_star, StarMul.star_mul, Set.mem_star, Set.star_mem_star, CStarMatrix.star_apply_of_isSelfAdjoint, QuaternionAlgebra.re_star, continuousAt_star, Set.star_subset_star, Set.star_mem_centralizer', ContinuousLinearMap.star_eq_adjoint, star_star_mul, CStarAlgebra.isStrictlyPositive_TFAE, derivWithin.star, isSelfAdjoint_iff, star_mul_self_sub_self_mul_star, fderiv_star, cfcₙ_star, SubStarSemigroup.star_mem', star_sub, IsIdempotentElem.star, unitary.expUnitary_eq_mul_inv, star_le_one_iff, Commute.star_right, ZeroAtInftyContinuousMap.star_apply, skewAdjoint.conjugate, NonUnitalStarAlgebra.star_self_mem_adjoin_singleton, StarSubalgebra.coe_centralizer, Matrix.conjTranspose_smul_non_comm, Unitary.symm_mulLeft, CStarMatrix.star_eq_conjTranspose, Unitary.mem_iff, intrinsicStar_def, Subalgebra.mem_star_iff, tsum_star, Matrix.conjTranspose_single, spinGroup.star_mul_self_of_mem, deriv_star_conj, star_right_conjugate_nonneg, LinearIsometryEquiv.star_eq_symm, Matrix.conjTranspose_vecMulVec, Units.embed_product_star, Module.End.isUnit_intrinsicStar_iff, Unitary.symm_mulRight_apply, Matrix.UnitaryGroup.map_star_coe, QuaternionAlgebra.star_smul, StarAlgebra.adjoin_eq_span, Matrix.conjTranspose_transpose, QuadraticAlgebra.norm_star, Unitization.norm_splitMul_snd_sq, Matrix.IsHermitian.star_mul_self_mul_eq_diagonal, Unitary.star_eq_inv, EuclideanSpace.inner_toLp_toLp, realPart_apply_coe, starLinearEquiv_apply, dotProduct_self_star_eq_zero, commute_star_comm, star_finsuppSum, QuadraticAlgebra.algebraMap_norm_eq_mul_star, Complex.UnitDisc.star_neg, conjugate_pos, Units.coe_star_inv, DifferentiableOn.star, star_zpow, Matrix.IsUnit.posSemidef_star_left_conjugate_iff, pinGroup.coe_star, Matrix.conjTranspose_smul, star_nonpos_iff, differentiable_star_iff, CStarAlgebra.star_right_conjugate_le_norm_smul, Complex.UnitDisc.star_eq_zero, Unitary.symm_mulLeft_apply, Continuous.star, LinearMap.isSymm_iff_basis, star_inj, starContinuousMap_apply, Prod.snd_star, CStarRing.nnnorm_self_mul_star, Complex.UnitDisc.star_zero, starRingEquiv_apply, CStarAlgebra.nonneg_TFAE, Matrix.updateRow_conjTranspose, pinGroup.coe_mul_star_self, summable_star_iff', cfcₙ_star_id, CFC.abs_mul_abs, star_natCast, lp.star_apply, LinearMap.intrinsicStar_comp, IsRegular.star, ContinuousAt.star, Quaternion.imJ_star, isUnit_star, star_div₀, star_le_star_iff, star_mul', star_zpow₀, conjugate_le_conjugate', Unitary.coe_star_mul_self, star_mul_self_pos, TensorProduct.star_map_apply_eq_map_intrinsicStar, CFC.norm_mul_mul_star_self_of_nonneg, cfc_star, IsUnit.mem_unitary_iff_mul_star_self, star_ratCast, Unitary.star_mem_iff, star_invOf, StarMonoidHom.map_star', Commute.star_left, Matrix.conjTranspose_smul_self, StarAlgHom.map_star', NonUnitalSubalgebra.starClosure_toNonUnitalSubalgebra, Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitary, Set.iInter_star, unitary.mul_star_self, spinGroup.coe_star, Prod.fst_star, unitary.star_mem_iff, MeasureTheory.AEEqFun.eLpNorm_star, NonUnitalStarAlgHom.map_star', star_nonneg_iff, starAddEquiv_apply, Complex.UnitDisc.coe_star, Unitary.coe_star, ContinuousLinearMap.intrinsicStar_apply, deriv.star', IsSelfAdjoint.conjugate, Set.star_empty, cfcₙ_comp_star, Subalgebra.star_mono, HasFDerivAt.star_star, Matrix.UnitaryGroup.star_mul_self, Matrix.conjTranspose_circulant, star_mem_iff, Unitary.conjStarAlgAut_star_apply, QuaternionAlgebra.imI_star, conjugate_nonneg, IsSelfAdjoint.conjugate', NonUnitalStarRingHom.map_star', IsSelfAdjoint.star_eq, Module.End.IsUnit.intrinsicStar, QuaternionAlgebra.star_mk, unitary.star_eq_inv, Quaternion.normSq_star, Unitization.fst_star, CStarRing.mul_star_self_eq_zero_iff, QuaternionAlgebra.star_eq_neg, Matrix.IsUnit.posDef_star_left_conjugate_iff, star_rat_smul, CStarRing.nnnorm_star_mul_self, star_left_conjugate_nonneg, isIdempotentElem_star_mul_self_iff_isIdempotentElem_self_mul_star, Unitary.star_eq_inv', Differentiable.star, Matrix.IsHermitian.star_eigenvectorUnitary_mulVec, InnerProductSpace.symm_toEuclideanLin_rankOne, MeasureTheory.Lp.coeFn_star, QuadraticAlgebra.im_star, NonUnitalSubalgebra.mem_starClosure, semiconjBy_star_star_star, Unitary.star_mem, IsUnit.mem_unitary_iff_star_mul_self, LinearMap.intrinsicStar_eq_comp, Unitary.path_apply, HasDerivAt.star_conj, star_one, Set.star_mul, star_inv, Matrix.diag_conjTranspose, Quaternion.star_coe, PositiveLinearMap.preGNS_norm_sq, pinGroup.mul_star_self_of_mem, Matrix.conjTranspose_replicateCol, IsUnit.isSelfAdjoint_conjugate_iff', unitary.star_mul_self, continuousWithinAt_star, Units.inv_mul_mem_unitary, DifferentiableWithinAt.star, Matrix.dotProduct_self_star_pos_iff, star_inv₀, conjugate_le_conjugate, star_neg_iff, Set.star_preimage, Matrix.IsHermitian.im_star_dotProduct_mulVec_self, MeasureTheory.StronglyMeasurable.star, Matrix.PosDef.dotProduct_mulVec_pos, algebraMap_star_comm, Matrix.UnitaryGroup.inv_apply, Matrix.IsUnit.posDef_star_right_conjugate_iff, spinGroup.star_mul_self, Matrix.PosDef.re_dotProduct_pos, spinGroup.star_mem_iff, ZeroAtInftyContinuousMap.coe_star, Quaternion.star_eq_self, unitary.mul_star_self_of_mem, NonUnitalSubalgebra.star_mem_star_iff, isSelfAdjoint_conjugate_iff_of_isUnit, Matrix.star_mulVec, Commute.star_star, HasStrictDerivAt.star, star_pow, Quaternion.norm_star, star_intCast_smul, NonUnitalSubalgebra.star_adjoin_comm

Summable

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalSummableSummable
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
HasSum.summable
HasSum.star
hasSum

SzemerediRegularity

Definitions

NameCategoryTheorems
star 📖CompOp
3 mathmath: biUnion_star_subset_nonuniformWitness, star_subset_chunk, card_biUnion_star_le_m_add_one_card_star_mul

deriv

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalderiv
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
ESeminormedAddMonoid.toAddMonoid
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
DFunLike.congr_fun
RingHomCompTriple.ids
RingHomInvPair.ids
fderiv_star

derivWithin

Theorems

NameKindAssumesProvesValidatesDepends On
star 📖mathematicalderivWithin
NormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
NormedAddCommGroup.toSeminormedAddCommGroup
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
ESeminormedAddMonoid.toAddMonoid
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
DFunLike.congr_fun
RingHomCompTriple.ids
RingHomInvPair.ids
fderivWithin_star
derivWithin_zero_of_not_uniqueDiffWithinAt
star_zero

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