Documentation Verification Report

Hom

📁 Source: Mathlib/GroupTheory/GroupAction/Hom.lean

Statistics

MetricCount
DefinitionsAddActionHom, comp, fst, id, instAddActionOfVAddCommClass, instCoeTCOfAddActionSemiHomClass, instVAddOfVAddCommClass, inverse, inverse', ofEq, prod, prodMap, snd, toFun, AddActionHomClass, AddActionSemiHomClass, toAddActionHom, DistribMulActionHom, comp, id, instCoeTCOfDistribMulActionSemiHomClassCoeMonoidHom, instFunLike, instInhabited, instOneId, instZero, inverse, toAddMonoidHom, toMulActionHom, DistribMulActionHomClass, DistribMulActionSemiHomClass, toDistribMulActionHom, MulActionHom, comp, fst, id, instAddCommGroup, instAddCommMonoid, instAddGroup, instAddMonoid, instAddZeroClass, instCoeTCOfMulActionSemiHomClass, instCommMonoid, instCommRing, instCommSemiring, instDistribMulActionOfSMulCommClass, instDistribSMulOfSMulCommClass, instModuleOfSMulCommClass, instMonoid, instMulActionOfSMulCommClass, instRing, instSMulOfSMulCommClass, instSemiring, instZero, inverse, inverse', ofEq, prod, prodMap, snd, toFun, MulActionHomClass, MulActionSemiHomClass, toMulActionHom, MulSemiringActionHom, comp, id, instCoeTCOfMulSemiringActionSemiHomClassCoeMonoidHom, instFunLike, inverse, inverse', toDistribMulActionHom, toRingHom, MulSemiringActionHomClass, toMulSemiringActionHom, MulSemiringActionSemiHomClass, evalAddActionHom, evalMulActionHom, toDistribMulActionHom, toMulActionHom, toAddActionHom, instFunLikeAddActionHom, instFunLikeMulActionHom, «AddActionHomIdLocal≺», «AddActionHomLocal≺», «DistribMulActionHomIdLocal≺», «DistribMulActionHomLocal≺», «MulActionHomIdLocal≺», «MulActionHomLocal≺», «MulSemiringActionHomIdLocal≺», «MulSemiringActionHomLocal≺»
90
Theoremscoe_vadd, comp_apply, comp_assoc, comp_id, comp_inverse', congr_fun, ext, ext_iff, fst_apply, fst_comp_prod, id_apply, id_comp, inverse'_apply, inverse'_comp, inverse'_inverse', inverse_apply, inverse_eq_inverse', map_vadd, map_vadd', ofEq_apply, ofEq_coe, prodMap_apply, prod_apply, prod_fst_snd, snd_apply, snd_comp_prod, map_vaddₛₗ, coe_fn_coe, coe_fn_coe', coe_one, coe_zero, comp_apply, comp_assoc, comp_id, congr_fun, ext, ext_iff, ext_ring, ext_ring_iff, id_apply, id_comp, instDistribMulActionSemiHomClassCoeMonoidHom, inverse_toFun, map_add, map_add', map_neg, map_smulₑ, map_sub, map_zero, map_zero', one_apply, toAddMonoidHom_injective, toFun_eq_coe, toMulActionHom_injective, zero_apply, toAddMonoidHomClass, toMulActionSemiHomClass, of_injective, of_injective, smulHomClass, coe_add, coe_mul, coe_neg, coe_one, coe_smul, coe_sub, coe_zero, comp_apply, comp_assoc, comp_id, comp_inverse', congr_fun, ext, ext_iff, fst_apply, fst_comp_prod, id_apply, id_comp, inverse'_apply, inverse'_comp, inverse'_inverse', inverse_apply, inverse_eq_inverse', map_smul, map_smul', ofEq_apply, ofEq_coe, prodMap_apply, prod_apply, prod_fst_snd, snd_apply, snd_comp_prod, map_smulₛₗ, coe_fn_coe, coe_fn_coe', comp_apply, comp_id, ext, ext_iff, id_apply, id_comp, instMulSemiringActionSemiHomClassCoeMonoidHom, inverse'_toFun, inverse_toFun, map_add, map_mul, map_mul', map_neg, map_one, map_one', map_smul, map_smulₛₗ, map_sub, map_zero, toDistribMulActionSemiHomClass, toMonoidHomClass, toRingHomClass, evalAddActionHom_apply, evalMulActionHom_apply, toDistribMulActionHom_toFun, toMulActionHom_apply, vaddHomClass, toAddActionHom_apply, instAddActionSemiHomClassAddActionHom, instMulActionSemiHomClassMulActionHom, map_smul, map_vadd
127
Total217

AddActionHom

Definitions

NameCategoryTheorems
comp 📖CompOp
9 mathmath: comp_assoc, SubAddAction.ofStabilizer.conjMap_comp, fst_comp_prod, inverse'_comp, snd_comp_prod, comp_inverse', comp_apply, comp_id, id_comp
fst 📖CompOp
3 mathmath: fst_comp_prod, fst_apply, prod_fst_snd
id 📖CompOp
6 mathmath: id_apply, inverse'_comp, comp_inverse', comp_id, prod_fst_snd, id_comp
instAddActionOfVAddCommClass 📖CompOp
instCoeTCOfAddActionSemiHomClass 📖CompOp
instVAddOfVAddCommClass 📖CompOp
1 mathmath: coe_vadd
inverse 📖CompOp
2 mathmath: inverse_eq_inverse', inverse_apply
inverse' 📖CompOp
5 mathmath: inverse'_inverse', inverse'_comp, inverse_eq_inverse', inverse'_apply, comp_inverse'
ofEq 📖CompOp
2 mathmath: ofEq_apply, ofEq_coe
prod 📖CompOp
4 mathmath: fst_comp_prod, snd_comp_prod, prod_fst_snd, prod_apply
prodMap 📖CompOp
1 mathmath: prodMap_apply
snd 📖CompOp
3 mathmath: snd_apply, snd_comp_prod, prod_fst_snd
toFun 📖CompOp
4 mathmath: ofEq_coe, Set.powersetCard.coe_addActionHom_of_embedding, map_vadd', SubAddAction.inclusion.toFun_eq_coe

Theorems

NameKindAssumesProvesValidatesDepends On
coe_vadd 📖mathematicalDFunLike.coe
AddActionHom
instFunLikeAddActionHom
HVAdd.hVAdd
instHVAdd
instVAddOfVAddCommClass
Pi.instVAdd
comp_apply 📖mathematicalDFunLike.coe
AddActionHom
instFunLikeAddActionHom
comp
comp_assoc 📖mathematicalcompext
comp_id 📖mathematicalcomp
id
CompTriple.instComp_id
CompTriple.instIsIdId
ext
CompTriple.instComp_id
CompTriple.instIsIdId
comp_apply
id_apply
comp_inverse' 📖mathematicalDFunLike.coe
AddActionHom
instFunLikeAddActionHom
comp
inverse'
CompTriple.comp_inv
CompTriple.instIsIdId
id
ext
CompTriple.comp_inv
CompTriple.instIsIdId
Function.LeftInverse.eq
congr_fun 📖mathematicalDFunLike.coe
AddActionHom
instFunLikeAddActionHom
DFunLike.congr_fun
ext 📖DFunLike.coe
AddActionHom
instFunLikeAddActionHom
DFunLike.ext
ext_iff 📖mathematicalDFunLike.coe
AddActionHom
instFunLikeAddActionHom
ext
fst_apply 📖mathematicalDFunLike.coe
AddActionHom
Prod.instVAdd
instFunLikeAddActionHom
fst
fst_comp_prod 📖mathematicalcomp
Prod.instVAdd
fst
prod
CompTriple.instId_comp
CompTriple.instIsIdId
CompTriple.instId_comp
CompTriple.instIsIdId
id_apply 📖mathematicalDFunLike.coe
AddActionHom
instFunLikeAddActionHom
id
id_comp 📖mathematicalcomp
id
CompTriple.instId_comp
CompTriple.instIsIdId
ext
CompTriple.instId_comp
CompTriple.instIsIdId
comp_apply
id_apply
inverse'_apply 📖mathematicalDFunLike.coe
AddActionHom
instFunLikeAddActionHom
inverse'
inverse'_comp 📖mathematicalDFunLike.coe
AddActionHom
instFunLikeAddActionHom
comp
inverse'
CompTriple.comp_inv
CompTriple.instIsIdId
id
ext
CompTriple.comp_inv
CompTriple.instIsIdId
Function.RightInverse.eq
inverse'_inverse' 📖mathematicalDFunLike.coe
AddActionHom
instFunLikeAddActionHom
inverse'ext
inverse_apply 📖mathematicalDFunLike.coe
AddActionHom
instFunLikeAddActionHom
inverse
inverse_eq_inverse' 📖mathematicalDFunLike.coe
AddActionHom
instFunLikeAddActionHom
inverse
inverse'
map_vadd 📖mathematicalDFunLike.coe
AddActionHom
instFunLikeAddActionHom
HVAdd.hVAdd
instHVAdd
map_vadd
instAddActionSemiHomClassAddActionHom
map_vadd' 📖mathematicaltoFun
HVAdd.hVAdd
instHVAdd
ofEq_apply 📖mathematicalDFunLike.coe
AddActionHom
instFunLikeAddActionHom
ofEq
ofEq_coe 📖mathematicaltoFun
ofEq
prodMap_apply 📖mathematicalDFunLike.coe
AddActionHom
Prod.instVAdd
instFunLikeAddActionHom
prodMap
prod_apply 📖mathematicalDFunLike.coe
AddActionHom
Prod.instVAdd
instFunLikeAddActionHom
prod
prod_fst_snd 📖mathematicalprod
Prod.instVAdd
fst
snd
id
snd_apply 📖mathematicalDFunLike.coe
AddActionHom
Prod.instVAdd
instFunLikeAddActionHom
snd
snd_comp_prod 📖mathematicalcomp
Prod.instVAdd
snd
prod
CompTriple.instId_comp
CompTriple.instIsIdId
CompTriple.instId_comp
CompTriple.instIsIdId

AddActionSemiHomClass

Definitions

NameCategoryTheorems
toAddActionHom 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
map_vaddₛₗ 📖mathematicalDFunLike.coe
HVAdd.hVAdd
instHVAdd

DistribMulActionHom

Definitions

NameCategoryTheorems
comp 📖CompOp
8 mathmath: MonoidAlgebra.distribMulActionHom_ext'_iff, comp_assoc, comp_apply, Finsupp.distribMulActionHom_ext'_iff, SkewMonoidAlgebra.distribMulActionHom_ext'_iff, AddMonoidAlgebra.distribMulActionHom_ext'_iff, comp_id, id_comp
id 📖CompOp
3 mathmath: id_apply, comp_id, id_comp
instCoeTCOfDistribMulActionSemiHomClassCoeMonoidHom 📖CompOp
instFunLike 📖CompOp
29 mathmath: one_apply, DomMulAct.smul_mulDistribActionHom_apply, MulSemiringActionHom.coe_fn_coe', congr_fun, coe_zero, SMulCommClass.toDistribMulActionHom_toFun, coe_fn_coe', id_apply, comp_apply, coe_one, instLinearMapClassId, IsModuleTopology.continuous_of_distribMulActionHomₑ, DomMulAct.mk_smul_mulDistribActionHom_apply, instDistribMulActionSemiHomClassCoeMonoidHom, coe_toLinearMap, zero_apply, ext_iff, map_neg, coe_fn_coe, IsModuleTopology.continuous_of_distribMulActionHom, map_smulₑ, toFun_eq_coe, ext_ring_iff, map_zero, map_add, map_sub, SkewMonoidAlgebra.DistribMulActionHom.single_toFun, instSemilinearMapClass, NonUnitalAlgHom.coe_to_distribMulActionHom
instInhabited 📖CompOp
instOneId 📖CompOp
2 mathmath: one_apply, coe_one
instZero 📖CompOp
2 mathmath: coe_zero, zero_apply
inverse 📖CompOp
1 mathmath: inverse_toFun
toAddMonoidHom 📖CompOp
toMulActionHom 📖CompOp
11 mathmath: WeakDual.CharacterSpace.toAlgHom_apply, PositiveLinearMap.gnsStarAlgHom_apply, MulSemiringActionHom.map_one', MulSemiringActionHom.map_mul', NonUnitalAlgHom.toFun_eq_coe, map_zero', map_add', NonUnitalAlgHom.map_mul', toFun_eq_coe, Pi.evalStarAlgHom_apply, NonUnitalStarAlgHom.map_star'

Theorems

NameKindAssumesProvesValidatesDepends On
coe_fn_coe 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddMonoidHom.instFunLike
AddMonoidHomClass.toAddMonoidHom
DistribMulActionHom
instFunLike
DistribMulActionSemiHomClass.toAddMonoidHomClass
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
MonoidHom.instFunLike
instDistribMulActionSemiHomClassCoeMonoidHom
DistribMulActionSemiHomClass.toAddMonoidHomClass
instDistribMulActionSemiHomClassCoeMonoidHom
coe_fn_coe' 📖mathematicalDFunLike.coe
MulActionHom
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
MonoidHom.instFunLike
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
instFunLikeMulActionHom
MulActionSemiHomClass.toMulActionHom
DistribMulActionHom
instFunLike
DistribMulActionSemiHomClass.toMulActionSemiHomClass
instDistribMulActionSemiHomClassCoeMonoidHom
DistribMulActionSemiHomClass.toMulActionSemiHomClass
instDistribMulActionSemiHomClassCoeMonoidHom
coe_one 📖mathematicalDFunLike.coe
DistribMulActionHom
MonoidHom.id
MulOneClass.toMulOne
Monoid.toMulOneClass
instFunLike
instOneId
coe_zero 📖mathematicalDFunLike.coe
DistribMulActionHom
instFunLike
instZero
Pi.instZero
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
comp_apply 📖mathematicalDFunLike.coe
DistribMulActionHom
instFunLike
comp
comp_assoc 📖mathematicalcompext
comp_id 📖mathematicalcomp
MonoidHom.id
MulOneClass.toMulOne
Monoid.toMulOneClass
id
MonoidHom.CompTriple.instComp_id
MonoidHom.CompTriple.instIsId
ext
MonoidHom.CompTriple.instComp_id
MonoidHom.CompTriple.instIsId
comp_apply
id_apply
congr_fun 📖mathematicalDFunLike.coe
DistribMulActionHom
instFunLike
DFunLike.congr_fun
ext 📖DFunLike.coe
DistribMulActionHom
instFunLike
DFunLike.ext
ext_iff 📖mathematicalDFunLike.coe
DistribMulActionHom
instFunLike
ext
ext_ring 📖DFunLike.coe
DistribMulActionHom
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
Module.toDistribMulAction
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toModule
instFunLike
AddMonoidWithOne.toOne
ext
mul_one
smul_eq_mul
map_smulₑ
ext_ring_iff 📖mathematicalDFunLike.coe
DistribMulActionHom
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
Module.toDistribMulAction
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toModule
instFunLike
AddMonoidWithOne.toOne
ext_ring
id_apply 📖mathematicalDFunLike.coe
DistribMulActionHom
MonoidHom.id
MulOneClass.toMulOne
Monoid.toMulOneClass
instFunLike
id
id_comp 📖mathematicalcomp
MonoidHom.id
MulOneClass.toMulOne
Monoid.toMulOneClass
id
MonoidHom.CompTriple.instId_comp
MonoidHom.CompTriple.instIsId
ext
MonoidHom.CompTriple.instId_comp
MonoidHom.CompTriple.instIsId
comp_apply
id_apply
instDistribMulActionSemiHomClassCoeMonoidHom 📖mathematicalDistribMulActionSemiHomClass
DistribMulActionHom
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
MonoidHom.instFunLike
instFunLike
MulActionHom.map_smul'
map_add'
map_zero'
inverse_toFun 📖mathematicalDFunLike.coe
DistribMulActionHom
MonoidHom.id
MulOneClass.toMulOne
Monoid.toMulOneClass
instFunLike
inverse
map_add 📖mathematicalDFunLike.coe
DistribMulActionHom
instFunLike
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
map_add
AddMonoidHomClass.toAddHomClass
DistribMulActionSemiHomClass.toAddMonoidHomClass
instDistribMulActionSemiHomClassCoeMonoidHom
map_add' 📖mathematicalMulActionHom.toFun
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
MonoidHom.instFunLike
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
toMulActionHom
AddZero.toAdd
map_neg 📖mathematicalDFunLike.coe
DistribMulActionHom
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instFunLike
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
map_neg
DistribMulActionSemiHomClass.toAddMonoidHomClass
instDistribMulActionSemiHomClassCoeMonoidHom
map_smulₑ 📖mathematicalDFunLike.coe
DistribMulActionHom
instFunLike
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
MonoidHom.instFunLike
MulActionSemiHomClass.map_smulₛₗ
DistribMulActionSemiHomClass.toMulActionSemiHomClass
instDistribMulActionSemiHomClassCoeMonoidHom
map_sub 📖mathematicalDFunLike.coe
DistribMulActionHom
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instFunLike
SubNegMonoid.toSub
map_sub
DistribMulActionSemiHomClass.toAddMonoidHomClass
instDistribMulActionSemiHomClassCoeMonoidHom
map_zero 📖mathematicalDFunLike.coe
DistribMulActionHom
instFunLike
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
map_zero
AddMonoidHomClass.toZeroHomClass
DistribMulActionSemiHomClass.toAddMonoidHomClass
instDistribMulActionSemiHomClassCoeMonoidHom
map_zero' 📖mathematicalMulActionHom.toFun
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
MonoidHom.instFunLike
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
toMulActionHom
one_apply 📖mathematicalDFunLike.coe
DistribMulActionHom
MonoidHom.id
MulOneClass.toMulOne
Monoid.toMulOneClass
instFunLike
instOneId
toAddMonoidHom_injective 📖AddMonoidHomClass.toAddMonoidHom
DistribMulActionHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
instFunLike
DistribMulActionSemiHomClass.toAddMonoidHomClass
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
MonoidHom.instFunLike
instDistribMulActionSemiHomClassCoeMonoidHom
DistribMulActionSemiHomClass.toAddMonoidHomClass
instDistribMulActionSemiHomClassCoeMonoidHom
ext
DFunLike.congr_fun
toFun_eq_coe 📖mathematicalMulActionHom.toFun
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
MonoidHom.instFunLike
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
toMulActionHom
DistribMulActionHom
instFunLike
toMulActionHom_injective 📖MulActionSemiHomClass.toMulActionHom
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
MonoidHom.instFunLike
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
DistribMulActionHom
instFunLike
DistribMulActionSemiHomClass.toMulActionSemiHomClass
instDistribMulActionSemiHomClassCoeMonoidHom
DistribMulActionSemiHomClass.toMulActionSemiHomClass
instDistribMulActionSemiHomClassCoeMonoidHom
ext
MulActionHom.congr_fun
zero_apply 📖mathematicalDFunLike.coe
DistribMulActionHom
instFunLike
instZero
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass

DistribMulActionSemiHomClass

Definitions

NameCategoryTheorems
toDistribMulActionHom 📖CompOp
4 mathmath: MulSemiringActionHom.coe_fn_coe', NonUnitalAlgHom.toDistribMulActionHom_eq_coe, NonUnitalAlgHom.coe_distribMulActionHom_mk, NonUnitalAlgHom.coe_to_distribMulActionHom

Theorems

NameKindAssumesProvesValidatesDepends On
toAddMonoidHomClass 📖mathematicalAddMonoidHomClass
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
toMulActionSemiHomClass 📖mathematicalMulActionSemiHomClass
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul

FaithfulSMul

Theorems

NameKindAssumesProvesValidatesDepends On
of_injective 📖mathematicalDFunLike.coeFaithfulSMuleq_of_smul_eq_smul
map_smul

IsSMulRegular

Theorems

NameKindAssumesProvesValidatesDepends On
of_injective 📖DFunLike.coe
IsSMulRegular
MulActionSemiHomClass.map_smulₛₗ

IsScalarTower

Theorems

NameKindAssumesProvesValidatesDepends On
smulHomClass 📖mathematicalMulActionHomClassmul_one
smul_eq_mul
map_smul
smul_assoc

MulActionHom

Definitions

NameCategoryTheorems
comp 📖CompOp
10 mathmath: id_comp, comp_apply, Set.powersetCard.mulActionHom_compl_mulActionHom_compl, snd_comp_prod, SubMulAction.ofStabilizer.conjMap_comp, comp_assoc, comp_id, fst_comp_prod, inverse'_comp, comp_inverse'
fst 📖CompOp
3 mathmath: fst_apply, prod_fst_snd, fst_comp_prod
id 📖CompOp
7 mathmath: id_comp, Set.powersetCard.mulActionHom_compl_mulActionHom_compl, comp_id, id_apply, prod_fst_snd, inverse'_comp, comp_inverse'
instAddCommGroup 📖CompOp
instAddCommMonoid 📖CompOp
instAddGroup 📖CompOp
2 mathmath: coe_sub, coe_neg
instAddMonoid 📖CompOp
instAddZeroClass 📖CompOp
1 mathmath: coe_add
instCoeTCOfMulActionSemiHomClass 📖CompOp
instCommMonoid 📖CompOp
instCommRing 📖CompOp
instCommSemiring 📖CompOp
instDistribMulActionOfSMulCommClass 📖CompOp
instDistribSMulOfSMulCommClass 📖CompOp
instModuleOfSMulCommClass 📖CompOp
instMonoid 📖CompOp
2 mathmath: coe_one, coe_mul
instMulActionOfSMulCommClass 📖CompOp
instRing 📖CompOp
instSMulOfSMulCommClass 📖CompOp
1 mathmath: coe_smul
instSemiring 📖CompOp
instZero 📖CompOp
1 mathmath: coe_zero
inverse 📖CompOp
2 mathmath: inverse_apply, inverse_eq_inverse'
inverse' 📖CompOp
5 mathmath: inverse'_apply, inverse'_inverse', inverse'_comp, inverse_eq_inverse', comp_inverse'
ofEq 📖CompOp
2 mathmath: ofEq_coe, ofEq_apply
prod 📖CompOp
4 mathmath: prod_apply, snd_comp_prod, prod_fst_snd, fst_comp_prod
prodMap 📖CompOp
1 mathmath: prodMap_apply
snd 📖CompOp
3 mathmath: snd_comp_prod, snd_apply, prod_fst_snd
toFun 📖CompOp
15 mathmath: ofEq_coe, SubMulAction.inclusion.toFun_eq_coe, WeakDual.CharacterSpace.toAlgHom_apply, map_smul', PositiveLinearMap.gnsStarAlgHom_apply, MulSemiringActionHom.map_one', MulSemiringActionHom.map_mul', NonUnitalAlgHom.toFun_eq_coe, DistribMulActionHom.map_zero', DistribMulActionHom.map_add', NonUnitalAlgHom.map_mul', DistribMulActionHom.toFun_eq_coe, Pi.evalStarAlgHom_apply, NonUnitalStarAlgHom.map_star', Set.powersetCard.coe_mulActionHom_of_embedding

Theorems

NameKindAssumesProvesValidatesDepends On
coe_add 📖mathematicalDFunLike.coe
MulActionHom
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
DistribSMul.toSMulZeroClass
instFunLikeMulActionHom
AddZero.toAdd
instAddZeroClass
Pi.instAdd
coe_mul 📖mathematicalDFunLike.coe
MulActionHom
SemigroupAction.toSMul
Monoid.toSemigroup
MulAction.toSemigroupAction
MulDistribMulAction.toMulAction
instFunLikeMulActionHom
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
instMonoid
Pi.instMul
coe_neg 📖mathematicalDFunLike.coe
MulActionHom
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
DistribSMul.toSMulZeroClass
instFunLikeMulActionHom
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
instAddGroup
Pi.instNeg
coe_one 📖mathematicalDFunLike.coe
MulActionHom
SemigroupAction.toSMul
Monoid.toSemigroup
MulAction.toSemigroupAction
MulDistribMulAction.toMulAction
instFunLikeMulActionHom
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
instMonoid
Pi.instOne
coe_smul 📖mathematicalDFunLike.coe
MulActionHom
instFunLikeMulActionHom
instSMulOfSMulCommClass
Pi.instSMul
coe_sub 📖mathematicalDFunLike.coe
MulActionHom
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
DistribSMul.toSMulZeroClass
instFunLikeMulActionHom
SubNegMonoid.toSub
instAddGroup
Pi.instSub
coe_zero 📖mathematicalDFunLike.coe
MulActionHom
SMulZeroClass.toSMul
instFunLikeMulActionHom
instZero
Pi.instZero
comp_apply 📖mathematicalDFunLike.coe
MulActionHom
instFunLikeMulActionHom
comp
comp_assoc 📖mathematicalcompext
comp_id 📖mathematicalcomp
id
CompTriple.instComp_id
CompTriple.instIsIdId
ext
CompTriple.instComp_id
CompTriple.instIsIdId
comp_apply
id_apply
comp_inverse' 📖mathematicalDFunLike.coe
MulActionHom
instFunLikeMulActionHom
comp
inverse'
CompTriple.comp_inv
CompTriple.instIsIdId
id
ext
CompTriple.comp_inv
CompTriple.instIsIdId
Function.LeftInverse.eq
congr_fun 📖mathematicalDFunLike.coe
MulActionHom
instFunLikeMulActionHom
DFunLike.congr_fun
ext 📖DFunLike.coe
MulActionHom
instFunLikeMulActionHom
DFunLike.ext
ext_iff 📖mathematicalDFunLike.coe
MulActionHom
instFunLikeMulActionHom
ext
fst_apply 📖mathematicalDFunLike.coe
MulActionHom
Prod.instSMul
instFunLikeMulActionHom
fst
fst_comp_prod 📖mathematicalcomp
Prod.instSMul
fst
prod
CompTriple.instId_comp
CompTriple.instIsIdId
CompTriple.instId_comp
CompTriple.instIsIdId
id_apply 📖mathematicalDFunLike.coe
MulActionHom
instFunLikeMulActionHom
id
id_comp 📖mathematicalcomp
id
CompTriple.instId_comp
CompTriple.instIsIdId
ext
CompTriple.instId_comp
CompTriple.instIsIdId
comp_apply
id_apply
inverse'_apply 📖mathematicalDFunLike.coe
MulActionHom
instFunLikeMulActionHom
inverse'
inverse'_comp 📖mathematicalDFunLike.coe
MulActionHom
instFunLikeMulActionHom
comp
inverse'
CompTriple.comp_inv
CompTriple.instIsIdId
id
ext
CompTriple.comp_inv
CompTriple.instIsIdId
Function.RightInverse.eq
inverse'_inverse' 📖mathematicalDFunLike.coe
MulActionHom
instFunLikeMulActionHom
inverse'ext
inverse_apply 📖mathematicalDFunLike.coe
MulActionHom
instFunLikeMulActionHom
inverse
inverse_eq_inverse' 📖mathematicalDFunLike.coe
MulActionHom
instFunLikeMulActionHom
inverse
inverse'
map_smul 📖mathematicalDFunLike.coe
MulActionHom
instFunLikeMulActionHom
map_smul
instMulActionSemiHomClassMulActionHom
map_smul' 📖mathematicaltoFun
ofEq_apply 📖mathematicalDFunLike.coe
MulActionHom
instFunLikeMulActionHom
ofEq
ofEq_coe 📖mathematicaltoFun
ofEq
prodMap_apply 📖mathematicalDFunLike.coe
MulActionHom
Prod.instSMul
instFunLikeMulActionHom
prodMap
prod_apply 📖mathematicalDFunLike.coe
MulActionHom
Prod.instSMul
instFunLikeMulActionHom
prod
prod_fst_snd 📖mathematicalprod
Prod.instSMul
fst
snd
id
snd_apply 📖mathematicalDFunLike.coe
MulActionHom
Prod.instSMul
instFunLikeMulActionHom
snd
snd_comp_prod 📖mathematicalcomp
Prod.instSMul
snd
prod
CompTriple.instId_comp
CompTriple.instIsIdId
CompTriple.instId_comp
CompTriple.instIsIdId

MulActionSemiHomClass

Definitions

NameCategoryTheorems
toMulActionHom 📖CompOp
1 mathmath: DistribMulActionHom.coe_fn_coe'

Theorems

NameKindAssumesProvesValidatesDepends On
map_smulₛₗ 📖mathematicalDFunLike.coe

MulSemiringActionHom

Definitions

NameCategoryTheorems
comp 📖CompOp
3 mathmath: comp_id, comp_apply, id_comp
id 📖CompOp
3 mathmath: comp_id, id_apply, id_comp
instCoeTCOfMulSemiringActionSemiHomClassCoeMonoidHom 📖CompOp
instFunLike 📖CompOp
17 mathmath: instMulSemiringActionSemiHomClassCoeMonoidHom, map_smulₛₗ, coe_fn_coe', id_apply, map_neg, map_sub, map_smul, comp_apply, coe_fn_coe, map_zero, IsInvariantSubring.coe_subtypeHom', coe_polynomial, map_one, map_mul, ext_iff, map_add, IsInvariantSubring.coe_subtypeHom
inverse 📖CompOp
1 mathmath: inverse_toFun
inverse' 📖CompOp
1 mathmath: inverse'_toFun
toDistribMulActionHom 📖CompOp
2 mathmath: map_one', map_mul'
toRingHom 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
coe_fn_coe 📖mathematicalDFunLike.coe
RingHom
Semiring.toNonAssocSemiring
RingHom.instFunLike
RingHomClass.toRingHom
MulSemiringActionHom
instFunLike
MulSemiringActionSemiHomClass.toRingHomClass
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
MonoidHom.instFunLike
MulSemiringAction.toDistribMulAction
instMulSemiringActionSemiHomClassCoeMonoidHom
MulSemiringActionSemiHomClass.toRingHomClass
instMulSemiringActionSemiHomClassCoeMonoidHom
coe_fn_coe' 📖mathematicalDFunLike.coe
DistribMulActionHom
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
MulSemiringAction.toDistribMulAction
DistribMulActionHom.instFunLike
DistribMulActionSemiHomClass.toDistribMulActionHom
MulSemiringActionHom
instFunLike
MulSemiringActionSemiHomClass.toDistribMulActionSemiHomClass
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
MonoidHom.instFunLike
instMulSemiringActionSemiHomClassCoeMonoidHom
MulSemiringActionSemiHomClass.toDistribMulActionSemiHomClass
instMulSemiringActionSemiHomClassCoeMonoidHom
comp_apply 📖mathematicalDFunLike.coe
MulSemiringActionHom
instFunLike
comp
comp_id 📖mathematicalcomp
MonoidHom.id
MulOneClass.toMulOne
Monoid.toMulOneClass
id
MonoidHom.CompTriple.instComp_id
MonoidHom.CompTriple.instIsId
ext
MonoidHom.CompTriple.instComp_id
MonoidHom.CompTriple.instIsId
comp_apply
id_apply
ext 📖DFunLike.coe
MulSemiringActionHom
instFunLike
DFunLike.ext
ext_iff 📖mathematicalDFunLike.coe
MulSemiringActionHom
instFunLike
ext
id_apply 📖mathematicalDFunLike.coe
MulSemiringActionHom
MonoidHom.id
MulOneClass.toMulOne
Monoid.toMulOneClass
instFunLike
id
id_comp 📖mathematicalcomp
MonoidHom.id
MulOneClass.toMulOne
Monoid.toMulOneClass
id
MonoidHom.CompTriple.instId_comp
MonoidHom.CompTriple.instIsId
ext
MonoidHom.CompTriple.instId_comp
MonoidHom.CompTriple.instIsId
comp_apply
id_apply
instMulSemiringActionSemiHomClassCoeMonoidHom 📖mathematicalMulSemiringActionSemiHomClass
MulSemiringActionHom
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
MonoidHom.instFunLike
MulSemiringAction.toDistribMulAction
instFunLike
MulActionHom.map_smul'
DistribMulActionHom.map_add'
DistribMulActionHom.map_zero'
map_mul'
map_one'
inverse'_toFun 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
MonoidHom.instFunLike
MulSemiringActionHom
instFunLike
inverse'
inverse_toFun 📖mathematicalDFunLike.coe
MulSemiringActionHom
MonoidHom.id
MulOneClass.toMulOne
Monoid.toMulOneClass
instFunLike
inverse
map_add 📖mathematicalDFunLike.coe
MulSemiringActionHom
instFunLike
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
map_add
AddMonoidHomClass.toAddHomClass
DistribMulActionSemiHomClass.toAddMonoidHomClass
MulSemiringActionSemiHomClass.toDistribMulActionSemiHomClass
instMulSemiringActionSemiHomClassCoeMonoidHom
map_mul 📖mathematicalDFunLike.coe
MulSemiringActionHom
instFunLike
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
map_mul
NonUnitalRingHomClass.toMulHomClass
RingHomClass.toNonUnitalRingHomClass
MulSemiringActionSemiHomClass.toRingHomClass
instMulSemiringActionSemiHomClassCoeMonoidHom
map_mul' 📖mathematicalMulActionHom.toFun
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
MonoidHom.instFunLike
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MulSemiringAction.toDistribMulAction
DistribMulActionHom.toMulActionHom
toDistribMulActionHom
MulOne.toMul
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
map_neg 📖mathematicalDFunLike.coe
MulSemiringActionHom
Ring.toSemiring
instFunLike
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
map_neg
DistribMulActionSemiHomClass.toAddMonoidHomClass
MulSemiringActionSemiHomClass.toDistribMulActionSemiHomClass
instMulSemiringActionSemiHomClassCoeMonoidHom
map_one 📖mathematicalDFunLike.coe
MulSemiringActionHom
instFunLike
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
RingHomClass.toMonoidWithZeroHomClass
MulSemiringActionSemiHomClass.toRingHomClass
instMulSemiringActionSemiHomClassCoeMonoidHom
map_one' 📖mathematicalMulActionHom.toFun
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
MonoidHom.instFunLike
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MulSemiringAction.toDistribMulAction
DistribMulActionHom.toMulActionHom
toDistribMulActionHom
MulOne.toOne
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
map_smul 📖mathematicalDFunLike.coe
MulSemiringActionHom
MonoidHom.id
MulOneClass.toMulOne
Monoid.toMulOneClass
instFunLike
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MulSemiringAction.toDistribMulAction
MulActionSemiHomClass.map_smulₛₗ
DistribMulActionSemiHomClass.toMulActionSemiHomClass
MulSemiringActionSemiHomClass.toDistribMulActionSemiHomClass
instMulSemiringActionSemiHomClassCoeMonoidHom
map_smulₛₗ 📖mathematicalDFunLike.coe
MulSemiringActionHom
instFunLike
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MulSemiringAction.toDistribMulAction
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
MonoidHom.instFunLike
MulActionSemiHomClass.map_smulₛₗ
DistribMulActionSemiHomClass.toMulActionSemiHomClass
MulSemiringActionSemiHomClass.toDistribMulActionSemiHomClass
instMulSemiringActionSemiHomClassCoeMonoidHom
map_sub 📖mathematicalDFunLike.coe
MulSemiringActionHom
Ring.toSemiring
instFunLike
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
map_sub
DistribMulActionSemiHomClass.toAddMonoidHomClass
MulSemiringActionSemiHomClass.toDistribMulActionSemiHomClass
instMulSemiringActionSemiHomClassCoeMonoidHom
map_zero 📖mathematicalDFunLike.coe
MulSemiringActionHom
instFunLike
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
map_zero
MonoidWithZeroHomClass.toZeroHomClass
RingHomClass.toMonoidWithZeroHomClass
MulSemiringActionSemiHomClass.toRingHomClass
instMulSemiringActionSemiHomClassCoeMonoidHom

MulSemiringActionHomClass

Definitions

NameCategoryTheorems
toMulSemiringActionHom 📖CompOp

MulSemiringActionSemiHomClass

Theorems

NameKindAssumesProvesValidatesDepends On
toDistribMulActionSemiHomClass 📖mathematicalDistribMulActionSemiHomClass
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
toMonoidHomClass 📖mathematicalMonoidHomClass
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
NonAssocSemiring.toMulZeroOneClass
Semiring.toNonAssocSemiring
toRingHomClass 📖mathematicalRingHomClass
Semiring.toNonAssocSemiring
toMonoidHomClass
DistribMulActionSemiHomClass.toAddMonoidHomClass
toDistribMulActionSemiHomClass

Pi

Definitions

NameCategoryTheorems
evalAddActionHom 📖CompOp
1 mathmath: evalAddActionHom_apply
evalMulActionHom 📖CompOp
1 mathmath: evalMulActionHom_apply

Theorems

NameKindAssumesProvesValidatesDepends On
evalAddActionHom_apply 📖mathematicalDFunLike.coe
AddActionHom
instVAdd
instFunLikeAddActionHom
evalAddActionHom
Function.eval
evalMulActionHom_apply 📖mathematicalDFunLike.coe
MulActionHom
instSMul
instFunLikeMulActionHom
evalMulActionHom
Function.eval

SMulCommClass

Definitions

NameCategoryTheorems
toDistribMulActionHom 📖CompOp
1 mathmath: toDistribMulActionHom_toFun
toMulActionHom 📖CompOp
1 mathmath: toMulActionHom_apply

Theorems

NameKindAssumesProvesValidatesDepends On
toDistribMulActionHom_toFun 📖mathematicalDFunLike.coe
DistribMulActionHom
MonoidHom.id
MulOneClass.toMulOne
Monoid.toMulOneClass
DistribMulActionHom.instFunLike
toDistribMulActionHom
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
toMulActionHom_apply 📖mathematicalDFunLike.coe
MulActionHom
instFunLikeMulActionHom
toMulActionHom

VAddAssocClass

Theorems

NameKindAssumesProvesValidatesDepends On
vaddHomClass 📖mathematicalAddActionHomClassadd_zero
vadd_eq_add
map_vadd
vadd_assoc

VAddCommClass

Definitions

NameCategoryTheorems
toAddActionHom 📖CompOp
1 mathmath: toAddActionHom_apply

Theorems

NameKindAssumesProvesValidatesDepends On
toAddActionHom_apply 📖mathematicalDFunLike.coe
AddActionHom
instFunLikeAddActionHom
toAddActionHom
HVAdd.hVAdd
instHVAdd

(root)

Definitions

NameCategoryTheorems
AddActionHom 📖CompData
38 mathmath: SubAddAction.subtype_apply, AddActionHom.id_apply, SubAddAction.ofFixingAddSubgroup_of_inclusion_injective, SubAddAction.subtype_eq_val, instAddActionSemiHomClassAddActionHom, SubAddAction.ofStabilizer.conjMap_comp_neg_apply, SubAddAction.conjMap_ofFixingAddSubgroup_bijective, AddActionHom.snd_apply, SubAddAction.conjMap_ofFixingAddSubgroup_coe_apply, Set.powersetCard.addActionHom_of_embedding_surjective, AddActionHom.ext_iff, AddActionHom.ofEq_apply, SubAddAction.SMulMemClass.coe_subtype, SubAddAction.ofFixingAddSubgroup_insert_map_bijective, AddActionHom.map_mem_fixedBy, Set.powersetCard.addActionHom_singleton_bijective, AddActionHom.map_vadd, SubAddAction.ofStabilizer.conjMap_bijective, SubAddAction.ofFixingAddSubgroup_insert_map_apply, SubAddAction.image_inclusion, AddActionHom.fst_apply, SubAddAction.ofFixingAddSubgroupEmpty_equivariantMap_bijective, SubAddAction.inclusion.coe_eq, SubAddAction.ofStabilizer.neg_conjMap_comp_apply, Pi.evalAddActionHom_apply, AddActionHom.comp_apply, AddActionHom.prodMap_apply, AddActionHom.congr_fun, SubAddAction.ofFixingAddSubgroup_equivariantMap_injective, AddActionHom.prod_apply, SubAddAction.ofStabilizer.conjMap_comp_apply, AddActionHom.map_mem_fixedPoints, SubAddAction.inclusion_injective, AddAction.IsBlock.preimage, AddActionHom.coe_vadd, VAddCommClass.toAddActionHom_apply, AddActionHom.zeroEmbeddingMap_bijective, SubAddAction.ofStabilizer.conjMap_apply
AddActionHomClass 📖MathDef
1 mathmath: VAddAssocClass.vaddHomClass
AddActionSemiHomClass 📖CompData
1 mathmath: instAddActionSemiHomClassAddActionHom
DistribMulActionHom 📖CompData
30 mathmath: DistribMulActionHom.one_apply, DomMulAct.smul_mulDistribActionHom_apply, MulSemiringActionHom.coe_fn_coe', DistribMulActionHom.congr_fun, DistribMulActionHom.coe_zero, SMulCommClass.toDistribMulActionHom_toFun, DistribMulActionHom.coe_fn_coe', DistribMulActionHom.id_apply, DomMulAct.instSMulCommClassDistribMulActionHomId, DistribMulActionHom.comp_apply, DistribMulActionHom.coe_one, DistribMulActionHom.instLinearMapClassId, IsModuleTopology.continuous_of_distribMulActionHomₑ, DomMulAct.mk_smul_mulDistribActionHom_apply, DistribMulActionHom.instDistribMulActionSemiHomClassCoeMonoidHom, DistribMulActionHom.coe_toLinearMap, DistribMulActionHom.zero_apply, DistribMulActionHom.ext_iff, DistribMulActionHom.map_neg, DistribMulActionHom.coe_fn_coe, IsModuleTopology.continuous_of_distribMulActionHom, DistribMulActionHom.map_smulₑ, DistribMulActionHom.toFun_eq_coe, DistribMulActionHom.ext_ring_iff, DistribMulActionHom.map_zero, DistribMulActionHom.map_add, DistribMulActionHom.map_sub, SkewMonoidAlgebra.DistribMulActionHom.single_toFun, DistribMulActionHom.instSemilinearMapClass, NonUnitalAlgHom.coe_to_distribMulActionHom
DistribMulActionHomClass 📖MathDef
DistribMulActionSemiHomClass 📖CompData
4 mathmath: NonUnitalAlgSemiHomClass.toDistribMulActionSemiHomClass, SemilinearMapClass.distribMulActionSemiHomClass, MulSemiringActionSemiHomClass.toDistribMulActionSemiHomClass, DistribMulActionHom.instDistribMulActionSemiHomClassCoeMonoidHom
MulActionHom 📖CompData
56 mathmath: SubMulAction.ofStabilizer.conjMap_comp_apply, SubMulAction.ofFixingSubgroup_insert_map_apply, MulActionHom.prod_apply, MulActionHom.coe_smul, SubMulAction.subtype_eq_val, SubMulAction.ofFixingSubgroup_equivariantMap_injective, SubMulAction.ofStabilizer.conjMap_comp_inv_apply, instMulActionSemiHomClassMulActionHom, SubMulAction.ofFixingSubgroup_of_inclusion_injective, Set.powersetCard.mem_mulActionHom_compl, SubMulAction.ofStabilizer.inv_conjMap_comp_apply, MulActionHom.map_smul, SubMulAction.subtype_injective, MulActionHom.prodMap_apply, MulActionHom.fst_apply, MulActionHom.coe_zero, MulActionHom.ofEq_apply, DistribMulActionHom.coe_fn_coe', SMulCommClass.toMulActionHom_apply, DomMulAct.smul_mulActionHom_apply, MulAction.IsBlock.preimage, MulActionHom.coe_sub, MulActionHom.coe_one, DomMulAct.instSMulCommClassMulActionHomId, MulActionHom.congr_fun, SubMulAction.inclusion_injective, MulActionHom.comp_apply, DomMulAct.mk_smul_mulActionHom_apply, SubMulAction.subtype_apply, MulActionHom.coe_mul, Set.powersetCard.mulActionHom_compl_bijective, MulActionHom.map_mem_fixedPoints, Pi.evalMulActionHom_apply, MulActionHom.toQuotient_apply, MulActionHom.coe_neg, SubMulAction.SMulMemClass.coe_subtype, SubMulAction.SMulMemClass.subtype_apply, SubMulAction.inclusion.coe_eq, MulActionHom.snd_apply, SubMulAction.ofFixingSubgroupEmpty_equivariantMap_bijective, Balanced.mulActionHom_preimage, Set.powersetCard.mulActionHom_singleton_bijective, SubMulAction.SMulMemClass.subtype_injective, MulActionHom.id_apply, Set.powersetCard.coe_mulActionHom_compl, MulActionHom.oneEmbeddingMap_bijective, SubMulAction.ofStabilizer.conjMap_bijective, MulActionHom.map_mem_fixedBy, MulActionHom.coe_add, SubMulAction.ofStabilizer.conjMap_apply, MulActionHom.ext_iff, SubMulAction.image_inclusion, Set.powersetCard.mulActionHom_of_embedding_surjective, SubMulAction.ofFixingSubgroup_insert_map_bijective, SubMulAction.conjMap_ofFixingSubgroup_bijective, SubMulAction.conjMap_ofFixingSubgroup_coe_apply
MulActionHomClass 📖MathDef
1 mathmath: IsScalarTower.smulHomClass
MulActionSemiHomClass 📖CompData
4 mathmath: instMulActionSemiHomClassMulActionHom, SemilinearMapClass.toMulActionSemiHomClass, NonUnitalAlgEquivClass.toMulActionSemiHomClass, DistribMulActionSemiHomClass.toMulActionSemiHomClass
MulSemiringActionHom 📖CompData
17 mathmath: MulSemiringActionHom.instMulSemiringActionSemiHomClassCoeMonoidHom, MulSemiringActionHom.map_smulₛₗ, MulSemiringActionHom.coe_fn_coe', MulSemiringActionHom.id_apply, MulSemiringActionHom.map_neg, MulSemiringActionHom.map_sub, MulSemiringActionHom.map_smul, MulSemiringActionHom.comp_apply, MulSemiringActionHom.coe_fn_coe, MulSemiringActionHom.map_zero, IsInvariantSubring.coe_subtypeHom', MulSemiringActionHom.coe_polynomial, MulSemiringActionHom.map_one, MulSemiringActionHom.map_mul, MulSemiringActionHom.ext_iff, MulSemiringActionHom.map_add, IsInvariantSubring.coe_subtypeHom
MulSemiringActionHomClass 📖MathDef
MulSemiringActionSemiHomClass 📖CompData
1 mathmath: MulSemiringActionHom.instMulSemiringActionSemiHomClassCoeMonoidHom
instFunLikeAddActionHom 📖CompOp
43 mathmath: SubAddAction.map_ofFixingAddSubgroupUnion_bijective, SubAddAction.subtype_apply, AddActionHom.id_apply, SubAddAction.ofFixingAddSubgroup_of_inclusion_injective, SubAddAction.subtype_eq_val, SubAddAction.ofFixingAddSubgroup_of_singleton_bijective, instAddActionSemiHomClassAddActionHom, SubAddAction.ofStabilizer.conjMap_comp_neg_apply, SubAddAction.conjMap_ofFixingAddSubgroup_bijective, AddActionHom.snd_apply, SubAddAction.conjMap_ofFixingAddSubgroup_coe_apply, Set.powersetCard.addActionHom_of_embedding_surjective, AddActionHom.ext_iff, AddActionHom.ofEq_apply, SubAddAction.ofFixingAddSubgroup_of_eq_bijective, SubAddAction.SMulMemClass.coe_subtype, SubAddAction.ofFixingAddSubgroup_insert_map_bijective, AddActionHom.map_mem_fixedBy, SubAddAction.ofFixingAddSubgroup_of_eq_apply, Set.powersetCard.addActionHom_singleton_bijective, AddActionHom.map_vadd, SubAddAction.ofStabilizer.conjMap_bijective, SubAddAction.ofFixingAddSubgroup_insert_map_apply, SubAddAction.image_inclusion, AddActionHom.fst_apply, SubAddAction.ofFixingAddSubgroupEmpty_equivariantMap_bijective, SubAddAction.inclusion.coe_eq, SubAddAction.ofStabilizer.neg_conjMap_comp_apply, Pi.evalAddActionHom_apply, AddActionHom.comp_apply, AddActionHom.prodMap_apply, AddActionHom.congr_fun, SubAddAction.ofFixingAddSubgroup_equivariantMap_injective, AddActionHom.prod_apply, SubAddAction.ofStabilizer.conjMap_comp_apply, AddActionHom.map_mem_fixedPoints, SubAddAction.inclusion_injective, AddAction.IsBlock.preimage, AddActionHom.coe_vadd, SubAddAction.map_ofFixingAddSubgroupUnion_def, VAddCommClass.toAddActionHom_apply, AddActionHom.zeroEmbeddingMap_bijective, SubAddAction.ofStabilizer.conjMap_apply
instFunLikeMulActionHom 📖CompOp
60 mathmath: SubMulAction.ofStabilizer.conjMap_comp_apply, SubMulAction.ofFixingSubgroup_insert_map_apply, MulActionHom.prod_apply, MulActionHom.coe_smul, SubMulAction.subtype_eq_val, SubMulAction.ofFixingSubgroup_equivariantMap_injective, SubMulAction.ofStabilizer.conjMap_comp_inv_apply, instMulActionSemiHomClassMulActionHom, SubMulAction.ofFixingSubgroup_of_inclusion_injective, Set.powersetCard.mem_mulActionHom_compl, SubMulAction.ofStabilizer.inv_conjMap_comp_apply, MulActionHom.map_smul, SubMulAction.map_ofFixingSubgroupUnion_def, SubMulAction.subtype_injective, MulActionHom.prodMap_apply, MulActionHom.fst_apply, MulActionHom.coe_zero, MulActionHom.ofEq_apply, DistribMulActionHom.coe_fn_coe', SMulCommClass.toMulActionHom_apply, DomMulAct.smul_mulActionHom_apply, MulAction.IsBlock.preimage, MulActionHom.coe_sub, MulActionHom.coe_one, MulActionHom.congr_fun, SubMulAction.inclusion_injective, MulActionHom.comp_apply, DomMulAct.mk_smul_mulActionHom_apply, SubMulAction.subtype_apply, MulActionHom.coe_mul, SubMulAction.ofFixingSubgroup_of_eq_apply, Set.powersetCard.mulActionHom_compl_bijective, MulActionHom.map_mem_fixedPoints, Pi.evalMulActionHom_apply, MulActionHom.toQuotient_apply, MulActionHom.coe_neg, SubMulAction.SMulMemClass.coe_subtype, SubMulAction.SMulMemClass.subtype_apply, SubMulAction.inclusion.coe_eq, SubMulAction.ofFixingSubgroup_of_singleton_bijective, MulActionHom.snd_apply, SubMulAction.ofFixingSubgroupEmpty_equivariantMap_bijective, Balanced.mulActionHom_preimage, SubMulAction.map_ofFixingSubgroupUnion_bijective, Set.powersetCard.mulActionHom_singleton_bijective, SubMulAction.ofFixingSubgroup_of_eq_bijective, SubMulAction.SMulMemClass.subtype_injective, MulActionHom.id_apply, Set.powersetCard.coe_mulActionHom_compl, MulActionHom.oneEmbeddingMap_bijective, SubMulAction.ofStabilizer.conjMap_bijective, MulActionHom.map_mem_fixedBy, MulActionHom.coe_add, SubMulAction.ofStabilizer.conjMap_apply, MulActionHom.ext_iff, SubMulAction.image_inclusion, Set.powersetCard.mulActionHom_of_embedding_surjective, SubMulAction.ofFixingSubgroup_insert_map_bijective, SubMulAction.conjMap_ofFixingSubgroup_bijective, SubMulAction.conjMap_ofFixingSubgroup_coe_apply
«AddActionHomIdLocal≺» 📖CompOp
«AddActionHomLocal≺» 📖CompOp
«DistribMulActionHomIdLocal≺» 📖CompOp
«DistribMulActionHomLocal≺» 📖CompOp
«MulActionHomIdLocal≺» 📖CompOp
«MulActionHomLocal≺» 📖CompOp
«MulSemiringActionHomIdLocal≺» 📖CompOp
«MulSemiringActionHomLocal≺» 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
instAddActionSemiHomClassAddActionHom 📖mathematicalAddActionSemiHomClass
AddActionHom
instFunLikeAddActionHom
AddActionHom.map_vadd'
instMulActionSemiHomClassMulActionHom 📖mathematicalMulActionSemiHomClass
MulActionHom
instFunLikeMulActionHom
MulActionHom.map_smul'
map_smul 📖mathematicalDFunLike.coeMulActionSemiHomClass.map_smulₛₗ
map_vadd 📖mathematicalDFunLike.coe
HVAdd.hVAdd
instHVAdd
AddActionSemiHomClass.map_vaddₛₗ

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