Documentation Verification Report

MonoidAlgebra

📁 Source: Mathlib/RingTheory/TensorProduct/MonoidAlgebra.lean

Statistics

MetricCount
DefinitionsscalarTensorEquiv, tensorEquiv, invFun, MonoidAlgebra, scalarTensorEquiv, tensorEquiv, invFun
7
TheoremsinstIsPushout, instIsPushout', scalarTensorEquiv_symm_single, scalarTensorEquiv_tmul, invFun_tmul, tensorEquiv_symm_single, tensorEquiv_tmul, instIsPushout, instIsPushout', scalarTensorEquiv_symm_single, scalarTensorEquiv_tmul, invFun_tmul, tensorEquiv_symm_single, tensorEquiv_tmul
14
Total21

AddMonoidAlgebra

Definitions

NameCategoryTheorems
scalarTensorEquiv 📖CompOp
2 mathmath: scalarTensorEquiv_symm_single, scalarTensorEquiv_tmul
tensorEquiv 📖CompOp
2 mathmath: tensorEquiv_tmul, tensorEquiv_symm_single

Theorems

NameKindAssumesProvesValidatesDepends On
instIsPushout 📖mathematicalAlgebra.IsPushout
AddMonoidAlgebra
CommSemiring.toSemiring
commSemiring
algebra
AddCommMonoid.toAddMonoid
algebraAddMonoidAlgebra
vaddAssocClass_addMonoidAlgebra
isScalarTower
DistribSMul.toSMulZeroClass
AddMonoid.toAddZeroClass
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Algebra.toModule
Algebra.toSMul
vaddAssocClass_addMonoidAlgebra
isScalarTower
IsBaseChange.of_equiv
Algebra.to_smulCommClass
induction_linear
RingHomInvPair.ids
RingHomCompTriple.ids
TensorProduct.tmul_zero
map_zero
MonoidWithZeroHomClass.toZeroHomClass
IsScalarTower.right
RingHomClass.toMonoidWithZeroHomClass
AlgHomClass.toRingHomClass
AlgEquivClass.toAlgHomClass
AlgEquiv.instAlgEquivClass
RingHom.instRingHomClass
tensorEquiv_tmul
map_add
SemilinearMapClass.toAddHomClass
NonUnitalAlgHomClass.instLinearMapClass
AlgHom.instNonUnitalAlgHomClassOfAlgHomClass
AlgHom.algHomClass
smul_add
one_smul
AddMonoidHomClass.toAddHomClass
RingHomClass.toAddMonoidHomClass
mapRangeAlgHom_single
mapRangeRingHom_single
Algebra.IsPushout.equiv_tmul
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
one_mul
instIsPushout' 📖mathematicalAlgebra.IsPushout
AddMonoidAlgebra
CommSemiring.toSemiring
commSemiring
algebra
AddCommMonoid.toAddMonoid
algebraAddMonoidAlgebra
isScalarTower
DistribSMul.toSMulZeroClass
AddMonoid.toAddZeroClass
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Algebra.toModule
Algebra.toSMul
vaddAssocClass_addMonoidAlgebra
Algebra.IsPushout.symm
vaddAssocClass_addMonoidAlgebra
isScalarTower
instIsPushout
scalarTensorEquiv_symm_single 📖mathematicalDFunLike.coe
AlgEquiv
AddMonoidAlgebra
CommSemiring.toSemiring
TensorProduct
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
addAddCommMonoid
Algebra.toModule
module
Semiring.toModule
semiring
AddCommMonoid.toAddMonoid
Algebra.TensorProduct.instSemiring
algebra
Algebra.id
Algebra.TensorProduct.leftAlgebra
Algebra.to_smulCommClass
AlgEquiv.instFunLike
AlgEquiv.symm
scalarTensorEquiv
single
TensorProduct.tmul
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Algebra.to_smulCommClass
mapRangeRingHom_single
AlgHomClass.toRingHomClass
tensorEquiv_symm_single
scalarTensorEquiv_tmul 📖mathematicalDFunLike.coe
AlgEquiv
TensorProduct
AddMonoidAlgebra
CommSemiring.toSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
addAddCommMonoid
Algebra.toModule
module
Semiring.toModule
Algebra.TensorProduct.instSemiring
semiring
AddCommMonoid.toAddMonoid
algebra
Algebra.id
Algebra.TensorProduct.leftAlgebra
Algebra.to_smulCommClass
AlgEquiv.instFunLike
scalarTensorEquiv
TensorProduct.tmul
Algebra.toSMul
AlgHom
AlgHom.funLike
mapRangeAlgHom
Algebra.ofId
ext
Algebra.to_smulCommClass
AlgHomClass.toRingHomClass
tensorEquiv_tmul
map_smul
SemilinearMapClass.toMulActionSemiHomClass
NonUnitalAlgHomClass.instLinearMapClass
AlgHom.instNonUnitalAlgHomClassOfAlgHomClass
AlgEquivClass.toAlgHomClass
AlgEquiv.instAlgEquivClass
mapRangeRingHom_apply
mapRangeAlgHom_apply
Algebra.mul_smul_comm
mul_one
Algebra.smul_def
Algebra.commutes
tensorEquiv_symm_single 📖mathematicalDFunLike.coe
AlgEquiv
AddMonoidAlgebra
TensorProduct
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Algebra.toModule
Algebra.TensorProduct.instSemiring
addAddCommMonoid
module
semiring
AddCommMonoid.toAddMonoid
algebra
Algebra.TensorProduct.leftAlgebra
Algebra.id
Algebra.to_smulCommClass
AlgEquiv.instFunLike
AlgEquiv.symm
tensorEquiv
single
TensorProduct.tmul
tensorEquiv.invFun_tmul
tensorEquiv_tmul 📖mathematicalDFunLike.coe
AlgEquiv
TensorProduct
AddMonoidAlgebra
CommSemiring.toSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
addAddCommMonoid
Algebra.toModule
module
Algebra.TensorProduct.instSemiring
semiring
AddCommMonoid.toAddMonoid
algebra
Algebra.TensorProduct.leftAlgebra
Algebra.id
Algebra.to_smulCommClass
AlgEquiv.instFunLike
tensorEquiv
TensorProduct.tmul
Algebra.toSMul
AlgHom
Algebra.TensorProduct.instAlgebra
AlgHom.funLike
mapRangeAlgHom
Algebra.TensorProduct.includeRight
Algebra.to_smulCommClass
CompTriple.comp_eq
CompTriple.instComp_id
CompTriple.instIsIdId
Algebra.smul_def

AddMonoidAlgebra.tensorEquiv

Definitions

NameCategoryTheorems
invFun 📖CompOp
1 mathmath: invFun_tmul

Theorems

NameKindAssumesProvesValidatesDepends On
invFun_tmul 📖mathematicalDFunLike.coe
AlgHom
AddMonoidAlgebra
TensorProduct
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Algebra.toModule
Algebra.TensorProduct.instSemiring
AddMonoidAlgebra.addAddCommMonoid
AddMonoidAlgebra.module
AddMonoidAlgebra.semiring
AddCommMonoid.toAddMonoid
AddMonoidAlgebra.algebra
Algebra.TensorProduct.leftAlgebra
Algebra.id
Algebra.to_smulCommClass
AlgHom.funLike
invFun
MonoidAlgebra.single
TensorProduct.tmul
MonoidAlgebra
MonoidAlgebra.addCommMonoid
Algebra.to_smulCommClass
DistribMulActionSemiHomClass.toAddMonoidHomClass
NonUnitalAlgSemiHomClass.toDistribMulActionSemiHomClass
AlgHom.instNonUnitalAlgHomClassOfAlgHomClass
AlgHom.algHomClass
AddMonoidAlgebra.liftNC_single
mul_one
AddMonoidAlgebra.single_mul_single
zero_add

MonoidAlgebra

Definitions

NameCategoryTheorems
scalarTensorEquiv 📖CompOp
2 mathmath: scalarTensorEquiv_tmul, scalarTensorEquiv_symm_single
tensorEquiv 📖CompOp
2 mathmath: tensorEquiv_symm_single, tensorEquiv_tmul

Theorems

NameKindAssumesProvesValidatesDepends On
instIsPushout 📖mathematicalAlgebra.IsPushout
MonoidAlgebra
CommSemiring.toSemiring
commSemiring
algebra
CommMonoid.toMonoid
algebraMonoidAlgebra
isScalarTower_monoidAlgebra
isScalarTower
DistribSMul.toSMulZeroClass
AddMonoid.toAddZeroClass
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Algebra.toModule
Algebra.toSMul
isScalarTower_monoidAlgebra
isScalarTower
IsBaseChange.of_equiv
Algebra.to_smulCommClass
induction_linear
RingHomInvPair.ids
RingHomCompTriple.ids
TensorProduct.tmul_zero
map_zero
MonoidWithZeroHomClass.toZeroHomClass
IsScalarTower.right
RingHomClass.toMonoidWithZeroHomClass
AlgHomClass.toRingHomClass
AlgEquivClass.toAlgHomClass
AlgEquiv.instAlgEquivClass
RingHom.instRingHomClass
tensorEquiv_tmul
map_add
SemilinearMapClass.toAddHomClass
NonUnitalAlgHomClass.instLinearMapClass
AlgHom.instNonUnitalAlgHomClassOfAlgHomClass
AlgHom.algHomClass
smul_add
one_smul
AddMonoidHomClass.toAddHomClass
RingHomClass.toAddMonoidHomClass
mapRangeAlgHom_single
mapRangeRingHom_single
Algebra.IsPushout.equiv_tmul
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
one_mul
instIsPushout' 📖mathematicalAlgebra.IsPushout
MonoidAlgebra
CommSemiring.toSemiring
commSemiring
algebra
CommMonoid.toMonoid
algebraMonoidAlgebra
isScalarTower
DistribSMul.toSMulZeroClass
AddMonoid.toAddZeroClass
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Module.toDistribMulAction
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Algebra.toModule
Algebra.toSMul
isScalarTower_monoidAlgebra
Algebra.IsPushout.symm
isScalarTower_monoidAlgebra
isScalarTower
instIsPushout
scalarTensorEquiv_symm_single 📖mathematicalDFunLike.coe
AlgEquiv
MonoidAlgebra
CommSemiring.toSemiring
TensorProduct
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
addCommMonoid
Algebra.toModule
module
Semiring.toModule
semiring
CommMonoid.toMonoid
Algebra.TensorProduct.instSemiring
algebra
Algebra.id
Algebra.TensorProduct.leftAlgebra
Algebra.to_smulCommClass
AlgEquiv.instFunLike
AlgEquiv.symm
scalarTensorEquiv
single
TensorProduct.tmul
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Algebra.to_smulCommClass
mapRangeRingHom_single
AlgHomClass.toRingHomClass
tensorEquiv_symm_single
scalarTensorEquiv_tmul 📖mathematicalDFunLike.coe
AlgEquiv
TensorProduct
MonoidAlgebra
CommSemiring.toSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
addCommMonoid
Algebra.toModule
module
Semiring.toModule
Algebra.TensorProduct.instSemiring
semiring
CommMonoid.toMonoid
algebra
Algebra.id
Algebra.TensorProduct.leftAlgebra
Algebra.to_smulCommClass
AlgEquiv.instFunLike
scalarTensorEquiv
TensorProduct.tmul
Algebra.toSMul
AlgHom
AlgHom.funLike
mapRangeAlgHom
Algebra.ofId
ext
Algebra.to_smulCommClass
AlgHomClass.toRingHomClass
tensorEquiv_tmul
map_smul
SemilinearMapClass.toMulActionSemiHomClass
NonUnitalAlgHomClass.instLinearMapClass
AlgHom.instNonUnitalAlgHomClassOfAlgHomClass
AlgEquivClass.toAlgHomClass
AlgEquiv.instAlgEquivClass
mapRangeRingHom_apply
mapRangeAlgHom_apply
Algebra.mul_smul_comm
mul_one
Algebra.smul_def
Algebra.commutes
tensorEquiv_symm_single 📖mathematicalDFunLike.coe
AlgEquiv
MonoidAlgebra
TensorProduct
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Algebra.toModule
Algebra.TensorProduct.instSemiring
addCommMonoid
module
semiring
CommMonoid.toMonoid
algebra
Algebra.TensorProduct.leftAlgebra
Algebra.id
Algebra.to_smulCommClass
AlgEquiv.instFunLike
AlgEquiv.symm
tensorEquiv
single
TensorProduct.tmul
tensorEquiv.invFun_tmul
tensorEquiv_tmul 📖mathematicalDFunLike.coe
AlgEquiv
TensorProduct
MonoidAlgebra
CommSemiring.toSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
addCommMonoid
Algebra.toModule
module
Algebra.TensorProduct.instSemiring
semiring
CommMonoid.toMonoid
algebra
Algebra.TensorProduct.leftAlgebra
Algebra.id
Algebra.to_smulCommClass
AlgEquiv.instFunLike
tensorEquiv
TensorProduct.tmul
Algebra.toSMul
AlgHom
Algebra.TensorProduct.instAlgebra
AlgHom.funLike
mapRangeAlgHom
Algebra.TensorProduct.includeRight
Algebra.to_smulCommClass
CompTriple.comp_eq
CompTriple.instComp_id
CompTriple.instIsIdId
Algebra.smul_def

MonoidAlgebra.tensorEquiv

Definitions

NameCategoryTheorems
invFun 📖CompOp
1 mathmath: invFun_tmul

Theorems

NameKindAssumesProvesValidatesDepends On
invFun_tmul 📖mathematicalDFunLike.coe
AlgHom
MonoidAlgebra
TensorProduct
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Algebra.toModule
Algebra.TensorProduct.instSemiring
MonoidAlgebra.addCommMonoid
MonoidAlgebra.module
MonoidAlgebra.semiring
CommMonoid.toMonoid
MonoidAlgebra.algebra
Algebra.TensorProduct.leftAlgebra
Algebra.id
Algebra.to_smulCommClass
AlgHom.funLike
invFun
MonoidAlgebra.single
TensorProduct.tmul
Algebra.to_smulCommClass
DistribMulActionSemiHomClass.toAddMonoidHomClass
NonUnitalAlgSemiHomClass.toDistribMulActionSemiHomClass
AlgHom.instNonUnitalAlgHomClassOfAlgHomClass
AlgHom.algHomClass
MonoidAlgebra.liftNC_single
mul_one
MonoidAlgebra.single_mul_single
one_mul

(root)

Definitions

NameCategoryTheorems
MonoidAlgebra 📖CompOp
255 mathmath: MonoidAlgebra.mapDomainRingEquiv_single, MonoidAlgebra.finiteType_of_fg, MonoidAlgebra.liftMagma_apply_apply, MonoidAlgebra.support_one_subset, Representation.IsIrreducible.instIsSimpleModuleMonoidAlgebraAsModule, Representation.ofMulActionSelfAsModuleEquiv_symm_apply, MonoidAlgebra.isLocalHom_algebraMap, MonoidAlgebra.mapRangeRingHom_single, MonoidAlgebra.Submodule.exists_isCompl, Representation.asAlgebraHom_single, MonoidAlgebra.algHom_ext'_iff, MonoidAlgebra.instIsCocomm, MonoidAlgebra.tensorEquiv.invFun_tmul, MonoidAlgebra.antipode_single, MonoidAlgebra.nontrivial, MonoidAlgebra.liftNC_mul, Subrepresentation.mem_ofSubmodule'_iff, MonoidAlgebra.cardinalMk_of_infinite, MonoidAlgebra.mul_def, MonoidAlgebra.domCongr_toAlgHom, Rep.to_Module_monoidAlgebra_map_aux, MonoidAlgebra.instIsCancelAdd, MonoidAlgebra.opRingEquiv_single, MonoidAlgebra.mapDomainRingHom_id, MonoidAlgebra.mapDomainRingEquiv_trans, MonoidAlgebra.single_one_mul_apply, MonoidAlgebra.single_eq_zero, MonoidAlgebra.mem_adjoin_support, Representation.asAlgebraHom_def, MonoidAlgebra.smulCommClass, MonoidAlgebra.opRingEquiv_symm_apply, MonoidAlgebra.of_mem_span_of_iff, MonoidAlgebra.symm_mapDomainAddEquiv, MonoidAlgebra.lift_symm_apply, MonoidAlgebra.uniqueRingEquiv_apply, MonoidAlgebra.coe_liftNCAlgHom, MonoidAlgebra.mapDomainNonUnitalRingHom_id, Representation.smul_ofModule_asModule, MonoidAlgebra.smulCommClass_self, MonoidAlgebra.instIsPushout, MonoidAlgebra.mapDomainAddEquiv_single, MonoidAlgebra.mapRangeRingEquiv_single, MonoidAlgebra.distribMulActionHom_ext'_iff, LinearMap.sumOfConjugatesEquivariant_apply, MonoidAlgebra.mapDomainBialgHom_comp, MonoidAlgebra.coe_algebraMap, MonoidAlgebra.mapDomain_algebraMap, Representation.ofMulAction_self_smul_eq_mul, MonoidAlgebra.single_mul_apply, FreeLieAlgebra.liftAux_map_smul, MonoidAlgebra.mapDomainBialgHom_mapDomainBialgHom, Representation.single_smul, MonoidAlgebra.mapRangeAlgHom_single, MonoidAlgebra.mapRangeAlgEquiv_trans, MonoidAlgebra.mvPolynomial_aeval_of_surjective_of_closure, MonoidAlgebra.domCongr_single, MonoidAlgebra.toRingHom_mapRangeAlgHom, MonoidAlgebra.scalarTensorEquiv_tmul, MonoidAlgebra.instFree, MonoidAlgebra.cardinalMk_lift_of_infinite, MonoidAlgebra.basis_apply, Rep.ofModuleMonoidAlgebra_obj_coe, MonoidAlgebra.single_algebraMap_eq_algebraMap_mul_of, MonoidAlgebra.liftNCRingHom_single, AddMonoidAlgebra.tensorEquiv.invFun_tmul, MonoidAlgebra.singleAddHom_apply, MonoidAlgebra.mapDomainAlgHom_id, MonoidAlgebra.mem_span_support, MonoidAlgebra.symm_mapRangeRingEquiv, MonoidAlgebra.faithfulSMul, MonoidAlgebra.coe_mapRangeRingHom, MonoidAlgebra.mapDomainAlgHom_comp, MonoidAlgebra.isLocalHom_singleOneRingHom, MonoidAlgebra.mapDomain_injective, Subrepresentation.mem_asSubmodule'_iff, MonoidAlgebra.intCast_def, MonoidAlgebra.mapRangeRingHom_comp_mapDomainRingHom, MonoidAlgebra.support_mul_single_eq_image, Representation.asModuleEquiv_symm_map_smul, MonoidAlgebra.mapRangeAlgHom_apply, MonoidAlgebra.symm_mapRangeAlgEquiv, MonoidAlgebra.lsingle_apply, MonoidAlgebra.single_mul_apply_aux, MonoidAlgebra.ofMagma_apply, MonoidAlgebra.lift_unique, MonoidAlgebra.tensorEquiv_symm_single, MonoidAlgebra.symm_commRingEquiv, MonoidAlgebra.lift_apply', Representation.isSemisimpleRepresentation_iff_isSemisimpleModule_asModule, Subrepresentation.submoduleSubrepresentationOrderIso_apply, MonoidAlgebra.mapDomainBialgHom_apply, MonoidAlgebra.opRingEquiv_symm_single, MonoidAlgebra.mapRangeAlgEquiv_apply, MonoidAlgebra.freeAlgebra_lift_of_surjective_of_closure, Representation.asAlgebraHom_single_one, MonoidAlgebra.ringHom_ext_iff, MonoidAlgebra.mapRangeRingHom_comp_algebraMap, MonoidAlgebra.smul_single, Representation.isSimpleModule_iff_irreducible_ofModule, Representation.instIsScalarTowerMonoidAlgebraAsModule, MonoidAlgebra.curryRingEquiv_symm_single, Subrepresentation.mem_asSubmodule_iff, MonoidAlgebra.mapRangeAddEquiv_apply, MonoidAlgebra.commAlgEquiv_single_single, MonoidAlgebra.mapDomainAddEquiv_trans, MonoidAlgebra.coe_add, MonoidAlgebra.isScalarTower_monoidAlgebra, MonoidAlgebra.isLocalHom_singleOneAlgHom, MonoidAlgebra.toRingHom_mapDomainRingEquiv, MonoidAlgebra.finiteType_iff_fg, MonoidAlgebra.moduleFinite, MonoidAlgebra.mul_apply_mul_eq_mul_of_uniqueMul, MonoidAlgebra.cardinalMk_of_infinite', MonoidAlgebra.single_mul_single, MonoidAlgebra.exists_finset_adjoin_eq_top, MonoidAlgebra.mapRangeAddEquiv_trans, MonoidAlgebra.smul_of, MonoidAlgebra.support_mul_single_subset, MonoidAlgebra.instIsCancelMulZeroOfIsCancelAddOfUniqueProds, Rep.ofModuleMonoidAlgebra_obj_ρ, RootPairing.isSimpleModule_weylGroupRootRep, Representation.ofMulActionSelfAsModuleEquiv_apply, LinearMap.conjugate_apply, CommRingCat.monoidAlgebra_map, MonoidAlgebra.liftNC_single, RootPairing.isSimpleModule_weylGroupRootRep_iff, MonoidAlgebra.smul_single', MonoidAlgebra.single_commute, Representation.asModuleEquiv_symm_map_rho, MonoidAlgebra.symm_mapRangeAddEquiv, Representation.ofModule_asModule_act, MonoidAlgebra.tensorEquiv_tmul, MonoidAlgebra.instNoZeroDivisorsOfUniqueProds, MonoidAlgebra.single_one_comm, MonoidAlgebra.sum_single, MonoidAlgebra.mapRangeRingEquiv_apply, Representation.asAlgebraHom_of, MonoidAlgebra.nonUnitalAlgHom_ext'_iff, MonoidAlgebra.smul_apply, MonoidAlgebra.singleHom_apply, MonoidAlgebra.mapDomainNonUnitalRingHom_apply, MonoidAlgebra.finiteType_iff_group_fg, MonoidAlgebra.domCongr_comp_lsingle, MonoidAlgebra.instIsPushout', MonoidAlgebra.instIsLeftCancelMulZeroOfIsCancelAddOfUniqueProds, MonoidAlgebra.support_mul_single, MonoidAlgebra.mul_single_apply_of_not_exists_mul, MonoidAlgebra.liftMagma_symm_apply, MonoidAlgebra.mul_single_one_apply, MonoidAlgebra.mapRangeRingEquiv_trans, MonoidAlgebra.domCongr_symm, LinearMap.equivariantProjection_apply, MonoidAlgebra.support_single_mul_eq_image, MonoidAlgebra.GroupSMul.linearMap_apply, MonoidAlgebra.lhom_ext'_iff, MonoidAlgebra.cardinalMk_lift_of_fintype, MonoidAlgebra.curryRingEquiv_single, MonoidAlgebra.scalarTensorEquiv_symm_single, MonoidAlgebra.of_commute, MonoidAlgebra.comul_single, Representation.smul_tprod_one_asModule, MonoidAlgebra.algebraMap_def, MonoidAlgebra.mem_ideal_span_of_image, MonoidAlgebra.lift_apply, MonoidAlgebra.lift_mapRangeRingHom_algebraMap, MonoidAlgebra.uniqueRingEquiv_symm_apply, MonoidAlgebra.of_injective, MonoidAlgebra.mapDomainRingHom_comp, MonoidAlgebra.support_single_mul, MonoidAlgebra.mul_apply, Rep.unit_iso_comm, MonoidAlgebra.mapDomainNonUnitalAlgHom_apply, MonoidAlgebra.singleOneRingHom_apply, MonoidAlgebra.mapDomainNonUnitalRingHom_comp, MonoidAlgebra.smulCommClass_symm_self, MonoidAlgebra.mapDomain_zero, MonoidAlgebra.mapDomain_one, FreeLieAlgebra.Rel.smulOfTower, Subrepresentation.subrepresentationSubmoduleOrderIso_symm_apply, Representation.ofModule_asAlgebraHom_apply_apply, MonoidAlgebra.symm_commAlgEquiv, MonoidAlgebra.single_zero, MonoidAlgebra.one_def, MonoidAlgebra.toRingHom_mapRangeRingEquiv, MonoidAlgebra.Submodule.instIsSemisimpleModule, MonoidAlgebra.liftNC_smul, MonoidAlgebra.mapDomainRingEquiv_apply, MonoidAlgebra.instIsRightCancelMulZeroOfIsCancelAddOfUniqueProds, MonoidAlgebra.single_commute_single, MonoidAlgebra.curryAlgEquiv_symm_single, MonoidAlgebra.instIsTorsionFree, MonoidAlgebra.ringHom_ext'_iff, MonoidAlgebra.single_add, MonoidAlgebra.single_eq_algebraMap_mul_of, MonoidAlgebra.mapRangeAddEquiv_single, MonoidAlgebra.single_neg, MonoidAlgebra.cardinalMk_lift_of_infinite', MonoidAlgebra.single_pow, Representation.irreducible_iff_isSimpleModule_asModule, MonoidAlgebra.isScalarTower_self, CommRingCat.monoidAlgebra_obj, GroupAlgebra.mul_average_left, MonoidAlgebra.domCongr_support, Representation.asModuleEquiv_map_smul, MonoidAlgebra.mul_apply_right, MonoidAlgebra.cardinalMk_of_fintype, MonoidAlgebra.symm_mapDomainRingEquiv, MonoidAlgebra.singleOneAlgHom_apply, MonoidAlgebra.lift_def, MonoidAlgebra.isCentralScalar, Representation.smul_one_tprod_asModule, Representation.is_simple_module_iff_irreducible_ofModule, MonoidAlgebra.isScalarTower, Subrepresentation.mem_ofSubmodule_iff, MonoidAlgebra.mapDomainAddEquiv_apply, MonoidAlgebra.mul_single_apply, MonoidAlgebra.mapRangeRingHom_id, MonoidAlgebra.mapDomainRingHom_apply, MonoidAlgebra.addHom_ext'_iff, Representation.free_asModule_free, MonoidAlgebra.mapDomain_sum, MonoidAlgebra.support_single_mul_subset, MonoidAlgebra.mul_apply_antidiagonal, MonoidAlgebra.mapDomain_mul, MonoidAlgebra.mapDomainAlgHom_apply, MonoidAlgebra.liftNC_one, MonoidAlgebra.mapDomainRingHom_comp_algebraMap, MonoidAlgebra.single_mul_apply_of_not_exists_mul, MonoidAlgebra.counit_single, MonoidAlgebra.support_mul, Subrepresentation.subrepresentationSubmoduleOrderIso_apply, Representation.asAlgebraHom_mem_of_forall_mem, MonoidAlgebra.opRingEquiv_apply, MonoidAlgebra.domCongr_refl, MonoidAlgebra.commRingEquiv_single_single, MonoidAlgebra.natCast_def, MonoidAlgebra.mapRangeRingHom_comp, MonoidAlgebra.domCongr_apply, MonoidAlgebra.mapDomainBialgHom_id, MonoidAlgebra.instIsDomainOfIsCancelAddOfUniqueProds, MonoidAlgebra.support_one, MonoidAlgebra.neg_apply, MonoidAlgebra.lift_single, MonoidAlgebra.curryAlgEquiv_single, MonoidAlgebra.of_apply, Representation.isSemisimpleModule_iff_isSemisimpleRepresentation_ofModule, MonoidAlgebra.mapDomain_add, Subrepresentation.submoduleSubrepresentationOrderIso_symm_apply, GroupAlgebra.mul_average_right, MonoidAlgebra.mul_single_apply_aux, MonoidAlgebra.lift_of, MonoidAlgebra.mapRangeRingHom_apply, MonoidAlgebra.lift_unique', MonoidAlgebra.prod_single, MonoidAlgebra.mul_apply_left

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