Documentation Verification Report

star

๐Ÿ“ Source: MathlibTest/LibrarySearch/star.lean

Statistics

MetricCount
Definitionsstar, star, star, star, star, star, star, star, star, star, star, star, star, star
14
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
Total48

CategoryTheory.Functor

Definitions

NameCategoryTheorems
star ๐Ÿ“–CompOp
4 mathmath: star_obj_as, FundamentalGroupoid.punitEquivDiscretePUnit_unitIso, FundamentalGroupoid.punitEquivDiscretePUnit_counitIso, FundamentalGroupoid.punitEquivDiscretePUnit_functor

CategoryTheory.MonoidalSingleObj

Definitions

NameCategoryTheorems
star ๐Ÿ“–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 ๐Ÿ“–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 ๐Ÿ“–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.ฯ€_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 ๐Ÿ“–mathematicalContinuousStar.starโ€”comp
ContinuousStar.continuous_star

ContinuousAt

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalContinuousAtStar.starโ€”comp
continuousAt_star

ContinuousOn

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalContinuousOnStar.starโ€”Continuous.comp_continuousOn
ContinuousStar.continuous_star

ContinuousWithinAt

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalContinuousWithinAtStar.starโ€”Filter.Tendsto.star

Differentiable

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalDifferentiable
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
โ€”DifferentiableAt.star

DifferentiableAt

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalDifferentiableAt
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
โ€”HasFDerivAt.differentiableAt
RingHomCompTriple.ids
RingHomInvPair.ids
HasFDerivAt.star
hasFDerivAt

DifferentiableOn

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalDifferentiableOn
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
โ€”DifferentiableWithinAt.star

DifferentiableWithinAt

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalDifferentiableWithinAt
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
โ€”HasFDerivWithinAt.differentiableWithinAt
RingHomCompTriple.ids
RingHomInvPair.ids
HasFDerivWithinAt.star
hasFDerivWithinAt

Equiv

Definitions

NameCategoryTheorems
star ๐Ÿ“–CompOpโ€”

Filter.EventuallyEq

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalFilter.EventuallyEqStar.star
Pi.instStarForall
โ€”fun_comp

Filter.Tendsto

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalFilter.Tendsto
nhds
Star.starโ€”comp
Continuous.tendsto
ContinuousStar.continuous_star

HasDerivAt

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–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
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
ESeminormedAddMonoid.toAddMonoid
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
โ€”IsBoundedSMul.continuousSMul
NormedSpace.toIsBoundedSMul
HasDerivAtFilter.star

HasDerivAtFilter

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–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
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
ESeminormedAddMonoid.toAddMonoid
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
โ€”IsBoundedSMul.continuousSMul
NormedSpace.toIsBoundedSMul
RingHomCompTriple.ids
RingHomInvPair.ids
congr_simp
one_smul
HasFDerivAtFilter.hasDerivAtFilter
HasFDerivAtFilter.star

HasDerivWithinAt

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–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
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
ESeminormedAddMonoid.toAddMonoid
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
โ€”IsBoundedSMul.continuousSMul
NormedSpace.toIsBoundedSMul
HasDerivAtFilter.star

HasFDerivAt

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalHasFDerivAt
SeminormedAddCommGroup.toAddCommGroup
NormedAddCommGroup.toSeminormedAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
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'
โ€”HasFDerivAtFilter.star

HasFDerivAtFilter

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalHasFDerivAtFilter
SeminormedAddCommGroup.toAddCommGroup
NormedAddCommGroup.toSeminormedAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
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'
โ€”comp
RingHomInvPair.ids
ContinuousLinearMap.hasFDerivAtFilter
Filter.tendsto_map

HasFDerivWithinAt

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalHasFDerivWithinAt
SeminormedAddCommGroup.toAddCommGroup
NormedAddCommGroup.toSeminormedAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
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'
โ€”HasFDerivAtFilter.star

HasStrictDerivAt

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–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
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
ESeminormedAddMonoid.toAddMonoid
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
โ€”IsBoundedSMul.continuousSMul
NormedSpace.toIsBoundedSMul
RingHomCompTriple.ids
RingHomInvPair.ids
congr_simp
one_smul
HasStrictFDerivAt.hasStrictDerivAt
HasStrictFDerivAt.star

HasStrictFDerivAt

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalHasStrictFDerivAt
SeminormedAddCommGroup.toAddCommGroup
NormedAddCommGroup.toSeminormedAddCommGroup
NormedSpace.toModule
NontriviallyNormedField.toNormedField
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'
โ€”comp
RingHomInvPair.ids
ContinuousLinearMap.hasStrictFDerivAt

HasSum

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalHasSumStar.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
โ€”map
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
ContinuousStar.continuous_star

Invertible

Definitions

NameCategoryTheorems
star ๐Ÿ“–CompOpโ€”

IsIdempotentElem

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalIsIdempotentElemStar.star
InvolutiveStar.toStar
StarMul.toInvolutiveStar
โ€”star_iff

IsLeftRegular

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalIsLeftRegularIsRightRegular
Star.star
InvolutiveStar.toStar
StarMul.toInvolutiveStar
โ€”star_injective
StarMul.star_mul
star_star

IsRegular

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalIsRegularStar.star
InvolutiveStar.toStar
StarMul.toInvolutiveStar
โ€”IsRightRegular.star
right
IsLeftRegular.star
left

IsRightRegular

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalIsRightRegularIsLeftRegular
Star.star
InvolutiveStar.toStar
StarMul.toInvolutiveStar
โ€”star_injective
StarMul.star_mul
star_star

IsStarNormal

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalโ€”IsStarNormal
InvolutiveStar.toStar
StarMul.toInvolutiveStar
Star.star
โ€”star_star
star_comm_self'

IsUnit

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalIsUnitStar.star
InvolutiveStar.toStar
StarMul.toInvolutiveStar
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
โ€”โ€”

Lean.Meta.RefinedDiscrTree.Trie

Definitions

NameCategoryTheorems
star ๐Ÿ“–CompOpโ€”

Mathlib.Tactic.ExtractGoal

Definitions

NameCategoryTheorems
star ๐Ÿ“–CompOpโ€”

MeasureTheory.AEStronglyMeasurable

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalMeasureTheory.AEStronglyMeasurableStar.star
Pi.instStarForall
โ€”MeasureTheory.Measure.instOuterMeasureClass
MeasureTheory.StronglyMeasurable.star
Filter.EventuallyEq.star

MeasureTheory.MemLp

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalMeasureTheory.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
โ€”MeasureTheory.AEStronglyMeasurable.star
NormedStarGroup.to_continuousStar
MeasureTheory.eLpNorm_star

MeasureTheory.StronglyMeasurable

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalMeasureTheory.StronglyMeasurableStar.star
Pi.instStarForall
โ€”Filter.Tendsto.star
tendsto_approx

Prefunctor

Definitions

NameCategoryTheorems
star ๐Ÿ“–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 ๐Ÿ“–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 ๐Ÿ“–โ€”Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
StarRing.toStarAddMonoid
RingQuot.Rel
โ€”โ€”StarAddMonoid.star_add
StarMul.star_mul

Set

Definitions

NameCategoryTheorems
star ๐Ÿ“–CompOp
30 mathmath: image_star, 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 ๐Ÿ“–mathematicalโ€”Set.Finite
Star.star
Set
Set.star
InvolutiveStar.toStar
โ€”preimage
Function.Injective.injOn
star_injective

Set.Nonempty

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalSet.NonemptyStar.star
Set
Set.star
InvolutiveStar.toStar
โ€”Set.nonempty_star

SetTheory.PGame

Definitions

NameCategoryTheorems
star ๐Ÿ“–CompOp
17 mathmath: star_lf_zero, neg_star, star_moveRight, nim_one_equiv, Impartial.impartial_star, star_fuzzy_zero, star_leftMoves, birthday_star, grundyValue_star, zero_lf_star, star_fuzzy_down, star_fuzzy_up, up_moveRight, SetTheory.Game.birthday_star, star_moveLeft, down_moveLeft, star_rightMoves

Star

Definitions

NameCategoryTheorems
star ๐Ÿ“–CompOp
662 mathmath: unitary.spectrum.unitary_conjugate, ContinuousMapZero.coe_star, NonUnitalSubalgebra.coe_starClosure, Quaternion.star_mul_self, Quaternion.coe_normSq_add, unitary.star_eq_inv', Quaternion.star_imJ, 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, unitary.inv_mul_mem_iff, NumberField.mem_maximalRealSubfield_iff, Quaternion.star_imI, Complex.star_def, Subalgebra.star_adjoin_comm, LinearMap.intrinsicStar_mulRight, LE.le.star_eq, Module.End.spectrum_intrinsicStar, IsUnit.star_right_conjugate_nonneg_iff, IsCHSHTuple.Bโ‚€_sa, spinGroup.star_eq_inv', QuaternionAlgebra.mul_star_eq_coe, commute_star_star, 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_toMatrixโ‚‚_mulVec, Complex.UnitDisc.conj_neg, Set.nonempty_star, WithCStarModule.inner_def, Matrix.star_vec, unitary.coe_star_mul_self, deriv.star, star_star, MulOpposite.op_star, Pi.star_single, Unitary.inv_mul_mem_iff, Matrix.IsUnit.posSemidef_star_right_conjugate_iff, IsCHSHTuple.Bโ‚_sa, Pell.pellZd_sub, Quaternion.star_re, Set.star_centralizer, HasStrictFDerivAt.star, Memโ„“p.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, 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, 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, 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, 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, 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, unitary.mem_iff_star_mul_self, 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.Aโ‚_sa, PositiveLinearMap.preGNS_inner_def, 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, FreeMonoid.star_one, StarMemClass.star_mem, pinGroup.star_mem, star_neg, FreeAlgebra.star_ฮน, 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, NonUnitalStarSubsemiring.star_mem', Zsqrtd.star_mk, QuaternionAlgebra.star_eq_self, star_nnrat_smul, TrivialStar.star_trivial, MeasureTheory.eLpNorm_star, NonUnitalStarAlgebra.adjoin_eq_span, Zsqrtd.star_im, CliffordAlgebraQuaternion.ofQuaternion_star, Matrix.conjTranspose_replicateRow, LinearMap.IntrinsicStar.isSelfAdjoint_iff_map_star, LinearMap.intrinsicStar_comp', Matrix.schur_complement_eqโ‚‚โ‚‚, 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_innerโ‚›โ‚—_apply, star_lt_one_iff, star_inv_intCast_smul, CFC.abs_nnrpow_two_mul, Matrix.PosSemidef.toLinearMapโ‚‚'_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.Aโ‚€_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, star_nsmul, Unitary.conjStarAlgAut_apply, Quaternion.mul_star_eq_coe, QuadraticAlgebra.re_star, starโ‚—แตข_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_toMatrixโ‚‚_mulVec, Quaternion.normSq_add, mul_star_self_pos, 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_eqโ‚โ‚, EuclideanSpace.inner_eq_star_dotProduct, NonUnitalSubalgebra.coe_star, QuaternionAlgebra.self_add_star', star_qsmul, cfc_star_id, 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', Memโ„“p.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, conjugate_lt_conjugate, Complex.UnitDisc.re_star, Set.star_mem_center, spinGroup.star_mem, LinearMap.intrinsicStar_id, InnerProductSpace.toMatrix_rankOne, CliffordAlgebra.star_ฮน, 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, 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, Quaternion.star_imK, ContinuousWithinAt.star, MeasureTheory.AEEqFun.coeFn_star, Quaternion.im_star, coe_starโ‚—แตข, 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, skewAdjoint.conjugate', StarOrderedRing.nonneg_iff, cfc_unitary_iff, Matrix.conjTranspose_apply, Matrix.PosSemidef.dotProduct_mulVec_zero_iff, HasDerivWithinAt.star, CliffordAlgebra.star_algebraMap, BoundedContinuousFunction.star_mem_range_charAlgHom, cfcโ‚™_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.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, ContinuousLinearMap.star_eq_adjoint, star_star_mul, CStarAlgebra.isStrictlyPositive_TFAE, derivWithin.star, isSelfAdjoint_iff, fderiv_star, cfcโ‚™_star, SubStarSemigroup.star_mem', star_sub, IsIdempotentElem.star, unitary.expUnitary_eq_mul_inv, star_le_one_iff, ZeroAtInftyContinuousMap.star_apply, skewAdjoint.conjugate, NonUnitalStarAlgebra.star_self_mem_adjoin_singleton, StarSubalgebra.coe_centralizer, CStarMatrix.star_eq_conjTranspose, Unitary.mem_iff, Zsqrtd.star_re, Subalgebra.mem_star_iff, tsum_star, Matrix.conjTranspose_single, spinGroup.star_mul_self_of_mem, star_right_conjugate_nonneg, LinearIsometryEquiv.star_eq_symm, Matrix.conjTranspose_vecMulVec, Units.embed_product_star, Module.End.isUnit_intrinsicStar_iff, 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, 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', cfcโ‚™_star_id, CFC.abs_mul_abs, star_natCast, lp.star_apply, LinearMap.intrinsicStar_comp, IsRegular.star, ContinuousAt.star, Quaternion.imJ_star, isUnit_star, star_divโ‚€, star_le_star_iff, star_mul', star_zpowโ‚€, conjugate_le_conjugate', Unitary.coe_star_mul_self, star_mul_self_pos, TensorProduct.star_map_apply_eq_map_intrinsicStar, cfc_star, IsUnit.mem_unitary_iff_mul_star_self, star_ratCast, Unitary.star_mem_iff, star_invOf, StarMonoidHom.map_star', 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, deriv.star', IsSelfAdjoint.conjugate, Set.star_empty, 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, 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_invโ‚€, 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 ๐Ÿ“–mathematicalSummableStar.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
โ€”HasSum.summable
HasSum.star
hasSum

SzemerediRegularity

Definitions

NameCategoryTheorems
star ๐Ÿ“–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 ๐Ÿ“–mathematicalโ€”deriv
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
โ€”DFunLike.congr_fun
RingHomCompTriple.ids
RingHomInvPair.ids
fderiv_star

derivWithin

Theorems

NameKindAssumesProvesValidatesDepends On
star ๐Ÿ“–mathematicalโ€”derivWithin
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
โ€”DFunLike.congr_fun
RingHomCompTriple.ids
RingHomInvPair.ids
fderivWithin_star
derivWithin_zero_of_not_uniqueDiffWithinAt
star_zero

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