Documentation Verification Report

Basic

πŸ“ Source: Mathlib/GroupTheory/Coprod/Basic.lean

Statistics

MetricCount
DefinitionscoprodAssoc, coprodComm, coprodCongr, coprodPUnit, punitCoprod, Coprod, clift, fst, inl, inr, inst, instAddGroup, instAddZeroClass, instNeg, liftEquiv, map, mk, snd, swap, toProd, coprodCon, Coprod, clift, fst, inl, inr, inst, instGroup, instInv, instMulOneClass, liftEquiv, map, mk, snd, swap, toProd, Β«term_βˆ—_Β», coprodCon, coprodAssoc, coprodComm, coprodCongr, coprodPUnit, punitCoprod
43
TheoremscoprodAssoc_apply_inl_inl, coprodAssoc_apply_inl_inr, coprodAssoc_apply_inr, coprodAssoc_symm_apply_inl, coprodAssoc_symm_apply_inr_inl, coprodAssoc_symm_apply_inr_inr, coprodComm_apply, coprodComm_symm_apply, coprodCongr_apply, coprodCongr_symm_apply, coprodPUnit_apply, coprodPUnit_symm_apply, punitCoprod_apply, punitCoprod_symm_apply, clift_apply_inl, clift_apply_inr, clift_apply_mk, clift_comp_mk, clift_mk, closure_range_inl_union_inr, codisjoint_mrange_inl_mrange_inr, codisjoint_range_inl_range_inr, comp_lift, con_ker_mk, con_neg_add_cancel, fst_apply_inl, fst_apply_inr, fst_comp_inl, fst_comp_inr, fst_comp_swap, fst_comp_toProd, fst_prod_snd, fst_surjective, fst_swap, fst_toProd, hom_ext, hom_ext_iff, induction_on, induction_on', inl_injective, inr_injective, lift_apply_inl, lift_apply_inr, lift_apply_mk, lift_comp_inl, lift_comp_inr, lift_comp_swap, lift_inl_inr, lift_inr_inl, lift_swap, lift_unique, map_apply_inl, map_apply_inr, map_comp_inl, map_comp_inr, map_comp_map, map_id_id, map_map, map_mk_ofList, mclosure_range_inl_union_inr, mk_eq_mk, mk_of_inl, mk_of_inr, mk_of_neg_add, mk_surjective, mker_swap, mrange_eq, mrange_inl_sup_mrange_inr, mrange_lift, mrange_mk, mrange_swap, neg_def, prod_mk_fst_snd, range_eq, range_inl_sup_range_inr, range_lift, range_swap, snd_apply_inl, snd_apply_inr, snd_comp_inl, snd_comp_inr, snd_comp_swap, snd_comp_toProd, snd_surjective, snd_swap, snd_toProd, swap_bijective, swap_comp_inl, swap_comp_inr, swap_comp_map, swap_comp_swap, swap_eq_zero, swap_inj, swap_injective, swap_inl, swap_inr, swap_map, swap_surjective, swap_swap, toProd_apply_inl, toProd_apply_inr, toProd_comp_inl, toProd_comp_inr, toProd_surjective, clift_apply_inl, clift_apply_inr, clift_apply_mk, clift_comp_mk, clift_mk, closure_range_inl_union_inr, codisjoint_mrange_inl_mrange_inr, codisjoint_range_inl_range_inr, comp_lift, con_inv_mul_cancel, con_ker_mk, fst_apply_inl, fst_apply_inr, fst_comp_inl, fst_comp_inr, fst_comp_swap, fst_comp_toProd, fst_prod_snd, fst_surjective, fst_swap, fst_toProd, hom_ext, hom_ext_iff, induction_on, induction_on', inl_injective, inr_injective, inv_def, lift_apply_inl, lift_apply_inr, lift_apply_mk, lift_comp_inl, lift_comp_inr, lift_comp_swap, lift_inl_inr, lift_inr_inl, lift_swap, lift_unique, map_apply_inl, map_apply_inr, map_comp_inl, map_comp_inr, map_comp_map, map_id_id, map_map, map_mk_ofList, mclosure_range_inl_union_inr, mk_eq_mk, mk_of_inl, mk_of_inr, mk_of_inv_mul, mk_surjective, mker_swap, mrange_eq, mrange_inl_sup_mrange_inr, mrange_lift, mrange_mk, mrange_swap, prod_mk_fst_snd, range_eq, range_inl_sup_range_inr, range_lift, range_swap, snd_apply_inl, snd_apply_inr, snd_comp_inl, snd_comp_inr, snd_comp_swap, snd_comp_toProd, snd_surjective, snd_swap, snd_toProd, swap_bijective, swap_comp_inl, swap_comp_inr, swap_comp_map, swap_comp_swap, swap_eq_one, swap_inj, swap_injective, swap_inl, swap_inr, swap_map, swap_surjective, swap_swap, toProd_apply_inl, toProd_apply_inr, toProd_comp_inl, toProd_comp_inr, toProd_surjective, coprodAssoc_apply_inl_inl, coprodAssoc_apply_inl_inr, coprodAssoc_apply_inr, coprodAssoc_symm_apply_inl, coprodAssoc_symm_apply_inr_inl, coprodAssoc_symm_apply_inr_inr, coprodComm_apply, coprodComm_symm_apply, coprodCongr_apply, coprodCongr_symm_apply, coprodPUnit_apply, coprodPUnit_symm_apply, punitCoprod_apply, punitCoprod_symm_apply
208
Total251

AddEquiv

Definitions

NameCategoryTheorems
coprodAssoc πŸ“–CompOp
6 mathmath: coprodAssoc_apply_inr, coprodAssoc_symm_apply_inr_inr, coprodAssoc_apply_inl_inr, coprodAssoc_symm_apply_inl, coprodAssoc_apply_inl_inl, coprodAssoc_symm_apply_inr_inl
coprodComm πŸ“–CompOp
2 mathmath: coprodComm_apply, coprodComm_symm_apply
coprodCongr πŸ“–CompOp
2 mathmath: coprodCongr_apply, coprodCongr_symm_apply
coprodPUnit πŸ“–CompOp
2 mathmath: coprodPUnit_symm_apply, coprodPUnit_apply
punitCoprod πŸ“–CompOp
2 mathmath: punitCoprod_symm_apply, punitCoprod_apply

Theorems

NameKindAssumesProvesValidatesDepends On
coprodAssoc_apply_inl_inl πŸ“–mathematicalβ€”DFunLike.coe
AddEquiv
AddMonoid.Coprod
AddMonoid.toAddZeroClass
AddMonoid.Coprod.instAddZeroClass
AddZero.toAdd
AddZeroClass.toAddZero
EquivLike.toFunLike
instEquivLike
coprodAssoc
AddMonoidHom
AddMonoidHom.instFunLike
AddMonoid.Coprod.inl
β€”β€”
coprodAssoc_apply_inl_inr πŸ“–mathematicalβ€”DFunLike.coe
AddEquiv
AddMonoid.Coprod
AddMonoid.toAddZeroClass
AddMonoid.Coprod.instAddZeroClass
AddZero.toAdd
AddZeroClass.toAddZero
EquivLike.toFunLike
instEquivLike
coprodAssoc
AddMonoidHom
AddMonoidHom.instFunLike
AddMonoid.Coprod.inl
AddMonoid.Coprod.inr
β€”β€”
coprodAssoc_apply_inr πŸ“–mathematicalβ€”DFunLike.coe
AddEquiv
AddMonoid.Coprod
AddMonoid.toAddZeroClass
AddMonoid.Coprod.instAddZeroClass
AddZero.toAdd
AddZeroClass.toAddZero
EquivLike.toFunLike
instEquivLike
coprodAssoc
AddMonoidHom
AddMonoidHom.instFunLike
AddMonoid.Coprod.inr
β€”β€”
coprodAssoc_symm_apply_inl πŸ“–mathematicalβ€”DFunLike.coe
AddEquiv
AddMonoid.Coprod
AddMonoid.toAddZeroClass
AddMonoid.Coprod.instAddZeroClass
AddZero.toAdd
AddZeroClass.toAddZero
EquivLike.toFunLike
instEquivLike
symm
coprodAssoc
AddMonoidHom
AddMonoidHom.instFunLike
AddMonoid.Coprod.inl
β€”β€”
coprodAssoc_symm_apply_inr_inl πŸ“–mathematicalβ€”DFunLike.coe
AddEquiv
AddMonoid.Coprod
AddMonoid.toAddZeroClass
AddMonoid.Coprod.instAddZeroClass
AddZero.toAdd
AddZeroClass.toAddZero
EquivLike.toFunLike
instEquivLike
symm
coprodAssoc
AddMonoidHom
AddMonoidHom.instFunLike
AddMonoid.Coprod.inr
AddMonoid.Coprod.inl
β€”β€”
coprodAssoc_symm_apply_inr_inr πŸ“–mathematicalβ€”DFunLike.coe
AddEquiv
AddMonoid.Coprod
AddMonoid.toAddZeroClass
AddMonoid.Coprod.instAddZeroClass
AddZero.toAdd
AddZeroClass.toAddZero
EquivLike.toFunLike
instEquivLike
symm
coprodAssoc
AddMonoidHom
AddMonoidHom.instFunLike
AddMonoid.Coprod.inr
β€”β€”
coprodComm_apply πŸ“–mathematicalβ€”DFunLike.coe
AddEquiv
AddMonoid.Coprod
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.Coprod.instAddZeroClass
EquivLike.toFunLike
instEquivLike
coprodComm
AddMonoidHom
AddMonoidHom.instFunLike
AddMonoid.Coprod.swap
β€”β€”
coprodComm_symm_apply πŸ“–mathematicalβ€”DFunLike.coe
AddEquiv
AddMonoid.Coprod
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.Coprod.instAddZeroClass
EquivLike.toFunLike
instEquivLike
symm
coprodComm
AddMonoidHom
AddMonoidHom.instFunLike
AddMonoid.Coprod.swap
β€”β€”
coprodCongr_apply πŸ“–mathematicalβ€”DFunLike.coe
AddEquiv
AddMonoid.Coprod
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.Coprod.instAddZeroClass
EquivLike.toFunLike
instEquivLike
coprodCongr
AddMonoidHom
AddMonoidHom.instFunLike
AddMonoid.Coprod.map
AddMonoidHomClass.toAddMonoidHom
β€”β€”
coprodCongr_symm_apply πŸ“–mathematicalβ€”DFunLike.coe
AddEquiv
AddMonoid.Coprod
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.Coprod.instAddZeroClass
EquivLike.toFunLike
instEquivLike
symm
coprodCongr
AddMonoidHom
AddMonoidHom.instFunLike
AddMonoid.Coprod.map
AddMonoidHomClass.toAddMonoidHom
β€”β€”
coprodPUnit_apply πŸ“–mathematicalβ€”DFunLike.coe
AddEquiv
AddMonoid.Coprod
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.Coprod.instAddZeroClass
EquivLike.toFunLike
instEquivLike
coprodPUnit
AddMonoidHom
AddMonoidHom.instFunLike
AddMonoid.Coprod.fst
β€”β€”
coprodPUnit_symm_apply πŸ“–mathematicalβ€”DFunLike.coe
AddEquiv
AddMonoid.Coprod
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.Coprod.instAddZeroClass
EquivLike.toFunLike
instEquivLike
symm
coprodPUnit
AddMonoidHom
AddMonoidHom.instFunLike
AddMonoid.Coprod.inl
β€”β€”
punitCoprod_apply πŸ“–mathematicalβ€”DFunLike.coe
AddEquiv
AddMonoid.Coprod
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.Coprod.instAddZeroClass
EquivLike.toFunLike
instEquivLike
punitCoprod
AddMonoidHom
AddMonoidHom.instFunLike
AddMonoid.Coprod.snd
β€”β€”
punitCoprod_symm_apply πŸ“–mathematicalβ€”DFunLike.coe
AddEquiv
AddMonoid.Coprod
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
PUnit.addCommGroup
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.Coprod.instAddZeroClass
EquivLike.toFunLike
instEquivLike
symm
punitCoprod
AddMonoidHom
AddMonoidHom.instFunLike
AddMonoid.Coprod.inr
β€”β€”

AddMonoid

Definitions

NameCategoryTheorems
Coprod πŸ“–CompOp
99 mathmath: Coprod.swap_surjective, Coprod.swap_comp_inl, Coprod.lift_comp_inr, AddEquiv.coprodComm_apply, Coprod.swap_inj, Coprod.toProd_apply_inr, Coprod.mk_of_inr, Coprod.snd_apply_inr, Coprod.snd_comp_toProd, Coprod.toProd_comp_inr, Coprod.fst_swap, AddEquiv.coprodPUnit_symm_apply, Coprod.map_map, Coprod.swap_bijective, Coprod.snd_comp_inr, Coprod.lift_inr_inl, Coprod.neg_def, Coprod.fst_comp_swap, Coprod.clift_comp_mk, Coprod.mrange_lift, Coprod.fst_comp_toProd, Coprod.prod_mk_fst_snd, Coprod.map_id_id, Coprod.map_comp_map, Coprod.clift_mk, Coprod.lift_comp_inl, Coprod.hom_ext_iff, Coprod.inl_injective, Coprod.map_apply_inr, Coprod.snd_toProd, AddEquiv.coprodAssoc_apply_inr, Coprod.swap_injective, Coprod.snd_surjective, Coprod.snd_comp_swap, Coprod.range_eq, Coprod.fst_comp_inl, Coprod.fst_toProd, Coprod.map_comp_inl, Coprod.toProd_apply_inl, AddEquiv.coprodPUnit_apply, Coprod.lift_apply_inl, Coprod.fst_comp_inr, Coprod.mk_surjective, Coprod.mk_of_neg_add, AddEquiv.coprodAssoc_symm_apply_inr_inr, Coprod.lift_apply_inr, Coprod.codisjoint_mrange_inl_mrange_inr, Coprod.swap_eq_zero, Coprod.fst_prod_snd, Coprod.snd_apply_inl, Coprod.comp_lift, AddEquiv.coprodAssoc_apply_inl_inr, AddEquiv.coprodCongr_apply, Coprod.swap_map, Coprod.codisjoint_range_inl_range_inr, AddEquiv.coprodAssoc_symm_apply_inl, AddEquiv.punitCoprod_symm_apply, Coprod.inr_injective, Coprod.swap_comp_swap, Coprod.lift_inl_inr, Coprod.fst_apply_inl, Coprod.map_mk_ofList, Coprod.mk_eq_mk, Coprod.toProd_surjective, Coprod.lift_comp_swap, Coprod.fst_apply_inr, Coprod.swap_swap, Coprod.range_swap, Coprod.clift_apply_inl, Coprod.swap_inl, Coprod.range_lift, Coprod.snd_swap, Coprod.lift_apply_mk, Coprod.mrange_mk, Coprod.mrange_inl_sup_mrange_inr, Coprod.mclosure_range_inl_union_inr, Coprod.mker_swap, Coprod.clift_apply_mk, Coprod.fst_surjective, Coprod.map_apply_inl, Coprod.mrange_swap, Coprod.map_comp_inr, Coprod.mrange_eq, Coprod.toProd_comp_inl, Coprod.closure_range_inl_union_inr, AddEquiv.coprodAssoc_apply_inl_inl, Coprod.con_ker_mk, Coprod.clift_apply_inr, AddEquiv.coprodCongr_symm_apply, AddEquiv.coprodComm_symm_apply, Coprod.range_inl_sup_range_inr, Coprod.swap_inr, Coprod.snd_comp_inl, Coprod.lift_swap, AddEquiv.coprodAssoc_symm_apply_inr_inl, Coprod.swap_comp_map, Coprod.mk_of_inl, Coprod.swap_comp_inr, AddEquiv.punitCoprod_apply
coprodCon πŸ“–CompOp
3 mathmath: Coprod.mk_eq_mk, Coprod.con_ker_mk, Coprod.con_neg_add_cancel

AddMonoid.Coprod

Definitions

NameCategoryTheorems
clift πŸ“–CompOp
5 mathmath: clift_comp_mk, clift_mk, clift_apply_inl, clift_apply_mk, clift_apply_inr
fst πŸ“–CompOp
14 mathmath: fst_swap, fst_comp_swap, fst_comp_toProd, prod_mk_fst_snd, snd_comp_swap, fst_comp_inl, fst_toProd, AddEquiv.coprodPUnit_apply, fst_comp_inr, fst_prod_snd, fst_apply_inl, fst_apply_inr, snd_swap, fst_surjective
inl πŸ“–CompOp
34 mathmath: swap_comp_inl, AddEquiv.coprodPUnit_symm_apply, lift_inr_inl, clift_mk, lift_comp_inl, hom_ext_iff, inl_injective, range_eq, fst_comp_inl, map_comp_inl, toProd_apply_inl, lift_apply_inl, codisjoint_mrange_inl_mrange_inr, snd_apply_inl, AddEquiv.coprodAssoc_apply_inl_inr, codisjoint_range_inl_range_inr, AddEquiv.coprodAssoc_symm_apply_inl, lift_inl_inr, fst_apply_inl, clift_apply_inl, swap_inl, mrange_inl_sup_mrange_inr, mclosure_range_inl_union_inr, map_apply_inl, mrange_eq, toProd_comp_inl, closure_range_inl_union_inr, AddEquiv.coprodAssoc_apply_inl_inl, range_inl_sup_range_inr, swap_inr, snd_comp_inl, AddEquiv.coprodAssoc_symm_apply_inr_inl, mk_of_inl, swap_comp_inr
inr πŸ“–CompOp
34 mathmath: swap_comp_inl, lift_comp_inr, toProd_apply_inr, mk_of_inr, snd_apply_inr, toProd_comp_inr, snd_comp_inr, lift_inr_inl, clift_mk, hom_ext_iff, map_apply_inr, AddEquiv.coprodAssoc_apply_inr, range_eq, fst_comp_inr, AddEquiv.coprodAssoc_symm_apply_inr_inr, lift_apply_inr, codisjoint_mrange_inl_mrange_inr, AddEquiv.coprodAssoc_apply_inl_inr, codisjoint_range_inl_range_inr, AddEquiv.punitCoprod_symm_apply, inr_injective, lift_inl_inr, fst_apply_inr, swap_inl, mrange_inl_sup_mrange_inr, mclosure_range_inl_union_inr, map_comp_inr, mrange_eq, closure_range_inl_union_inr, clift_apply_inr, range_inl_sup_range_inr, swap_inr, AddEquiv.coprodAssoc_symm_apply_inr_inl, swap_comp_inr
inst πŸ“–CompOp
2 mathmath: lift_inr_inl, lift_inl_inr
instAddGroup πŸ“–CompOp
6 mathmath: range_eq, codisjoint_range_inl_range_inr, range_swap, range_lift, closure_range_inl_union_inr, range_inl_sup_range_inr
instAddZeroClass πŸ“–CompOp
94 mathmath: swap_surjective, swap_comp_inl, lift_comp_inr, AddEquiv.coprodComm_apply, swap_inj, toProd_apply_inr, mk_of_inr, snd_apply_inr, snd_comp_toProd, toProd_comp_inr, fst_swap, AddEquiv.coprodPUnit_symm_apply, map_map, swap_bijective, snd_comp_inr, neg_def, fst_comp_swap, clift_comp_mk, mrange_lift, fst_comp_toProd, prod_mk_fst_snd, map_id_id, map_comp_map, clift_mk, lift_comp_inl, hom_ext_iff, inl_injective, map_apply_inr, snd_toProd, AddEquiv.coprodAssoc_apply_inr, swap_injective, snd_surjective, snd_comp_swap, range_eq, fst_comp_inl, fst_toProd, map_comp_inl, toProd_apply_inl, AddEquiv.coprodPUnit_apply, lift_apply_inl, fst_comp_inr, mk_surjective, mk_of_neg_add, AddEquiv.coprodAssoc_symm_apply_inr_inr, lift_apply_inr, codisjoint_mrange_inl_mrange_inr, swap_eq_zero, fst_prod_snd, snd_apply_inl, comp_lift, AddEquiv.coprodAssoc_apply_inl_inr, AddEquiv.coprodCongr_apply, swap_map, AddEquiv.coprodAssoc_symm_apply_inl, AddEquiv.punitCoprod_symm_apply, inr_injective, swap_comp_swap, lift_inl_inr, fst_apply_inl, map_mk_ofList, mk_eq_mk, toProd_surjective, lift_comp_swap, fst_apply_inr, swap_swap, clift_apply_inl, swap_inl, snd_swap, lift_apply_mk, mrange_mk, mrange_inl_sup_mrange_inr, mclosure_range_inl_union_inr, mker_swap, clift_apply_mk, fst_surjective, map_apply_inl, mrange_swap, map_comp_inr, mrange_eq, toProd_comp_inl, closure_range_inl_union_inr, AddEquiv.coprodAssoc_apply_inl_inl, con_ker_mk, clift_apply_inr, AddEquiv.coprodCongr_symm_apply, AddEquiv.coprodComm_symm_apply, swap_inr, snd_comp_inl, lift_swap, AddEquiv.coprodAssoc_symm_apply_inr_inl, swap_comp_map, mk_of_inl, swap_comp_inr, AddEquiv.punitCoprod_apply
instNeg πŸ“–CompOp
1 mathmath: neg_def
liftEquiv πŸ“–CompOpβ€”
map πŸ“–CompOp
12 mathmath: map_map, map_id_id, map_comp_map, map_apply_inr, map_comp_inl, AddEquiv.coprodCongr_apply, swap_map, map_mk_ofList, map_apply_inl, map_comp_inr, AddEquiv.coprodCongr_symm_apply, swap_comp_map
mk πŸ“–CompOpβ€”
snd πŸ“–CompOp
14 mathmath: snd_apply_inr, snd_comp_toProd, fst_swap, snd_comp_inr, fst_comp_swap, prod_mk_fst_snd, snd_toProd, snd_surjective, snd_comp_swap, fst_prod_snd, snd_apply_inl, snd_swap, snd_comp_inl, AddEquiv.punitCoprod_apply
swap πŸ“–CompOp
25 mathmath: swap_surjective, swap_comp_inl, AddEquiv.coprodComm_apply, swap_inj, fst_swap, swap_bijective, lift_inr_inl, fst_comp_swap, swap_injective, snd_comp_swap, swap_eq_zero, swap_map, swap_comp_swap, lift_comp_swap, swap_swap, range_swap, swap_inl, snd_swap, mker_swap, mrange_swap, AddEquiv.coprodComm_symm_apply, swap_inr, lift_swap, swap_comp_map, swap_comp_inr
toProd πŸ“–CompOp
11 mathmath: toProd_apply_inr, snd_comp_toProd, toProd_comp_inr, fst_comp_toProd, prod_mk_fst_snd, snd_toProd, fst_toProd, toProd_apply_inl, fst_prod_snd, toProd_surjective, toProd_comp_inl

Theorems

NameKindAssumesProvesValidatesDepends On
clift_apply_inl πŸ“–mathematicalDFunLike.coe
AddMonoidHom
FreeAddMonoid
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
FreeAddMonoid.instAddCancelMonoid
AddMonoidHom.instFunLike
FreeAddMonoid.of
AddZero.toZero
AddZero.toAdd
AddMonoid.Coprod
instAddZeroClass
clift
inl
β€”β€”
clift_apply_inr πŸ“–mathematicalDFunLike.coe
AddMonoidHom
FreeAddMonoid
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
FreeAddMonoid.instAddCancelMonoid
AddMonoidHom.instFunLike
FreeAddMonoid.of
AddZero.toZero
AddZero.toAdd
AddMonoid.Coprod
instAddZeroClass
clift
inr
β€”β€”
clift_apply_mk πŸ“–mathematicalDFunLike.coe
AddMonoidHom
FreeAddMonoid
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
FreeAddMonoid.instAddCancelMonoid
AddMonoidHom.instFunLike
FreeAddMonoid.of
AddZero.toZero
AddZero.toAdd
AddMonoid.Coprod
instAddZeroClass
clift
β€”β€”
clift_comp_mk πŸ“–mathematicalDFunLike.coe
AddMonoidHom
FreeAddMonoid
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
FreeAddMonoid.instAddCancelMonoid
AddMonoidHom.instFunLike
FreeAddMonoid.of
AddZero.toZero
AddZero.toAdd
AddMonoidHom.comp
AddMonoid.Coprod
instAddZeroClass
clift
β€”DFunLike.ext'
clift_mk πŸ“–mathematicalβ€”clift
AddMonoid.Coprod
instAddZeroClass
map_zero
AddMonoidHom
AddZeroClass.toAddZero
AddZero.toZero
AddMonoidHom.instFunLike
AddMonoidHomClass.toZeroHomClass
AddMonoidHom.instAddMonoidHomClass
inl
inr
map_add
AddZero.toAdd
AddMonoidHomClass.toAddHomClass
AddMonoidHom.id
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inl
β€”β€”
swap_comp_map πŸ“–mathematicalβ€”AddMonoidHom.comp
AddMonoid.Coprod
AddZeroClass.toAddZero
instAddZeroClass
swap
map
β€”hom_ext
swap_comp_swap πŸ“–mathematicalβ€”AddMonoidHom.comp
AddMonoid.Coprod
AddZeroClass.toAddZero
instAddZeroClass
swap
AddMonoidHom.id
β€”hom_ext
swap_eq_zero πŸ“–mathematicalβ€”DFunLike.coe
AddMonoidHom
AddMonoid.Coprod
AddZeroClass.toAddZero
instAddZeroClass
AddMonoidHom.instFunLike
swap
AddZero.toZero
β€”swap_injective
map_zero
AddMonoidHomClass.toZeroHomClass
AddMonoidHom.instAddMonoidHomClass
swap_inj πŸ“–mathematicalβ€”DFunLike.coe
AddMonoidHom
AddMonoid.Coprod
AddZeroClass.toAddZero
instAddZeroClass
AddMonoidHom.instFunLike
swap
β€”swap_injective
swap_injective πŸ“–mathematicalβ€”AddMonoid.Coprod
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
instAddZeroClass
AddMonoidHom.instFunLike
swap
β€”swap_swap
swap_inl πŸ“–mathematicalβ€”DFunLike.coe
AddMonoidHom
AddMonoid.Coprod
AddZeroClass.toAddZero
instAddZeroClass
AddMonoidHom.instFunLike
swap
inl
inr
β€”β€”
swap_inr πŸ“–mathematicalβ€”DFunLike.coe
AddMonoidHom
AddMonoid.Coprod
AddZeroClass.toAddZero
instAddZeroClass
AddMonoidHom.instFunLike
swap
inr
inl
β€”β€”
swap_map πŸ“–mathematicalβ€”DFunLike.coe
AddMonoidHom
AddMonoid.Coprod
AddZeroClass.toAddZero
instAddZeroClass
AddMonoidHom.instFunLike
swap
map
β€”DFunLike.congr_fun
swap_comp_map
swap_surjective πŸ“–mathematicalβ€”AddMonoid.Coprod
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
instAddZeroClass
AddMonoidHom.instFunLike
swap
β€”Function.LeftInverse.surjective
swap_swap
swap_swap πŸ“–mathematicalβ€”DFunLike.coe
AddMonoidHom
AddMonoid.Coprod
AddZeroClass.toAddZero
instAddZeroClass
AddMonoidHom.instFunLike
swap
β€”DFunLike.congr_fun
swap_comp_swap
toProd_apply_inl πŸ“–mathematicalβ€”DFunLike.coe
AddMonoidHom
AddMonoid.Coprod
AddMonoid.toAddZeroClass
AddZeroClass.toAddZero
instAddZeroClass
Prod.instAddZeroClass
AddMonoidHom.instFunLike
toProd
inl
AddZero.toZero
β€”β€”
toProd_apply_inr πŸ“–mathematicalβ€”DFunLike.coe
AddMonoidHom
AddMonoid.Coprod
AddMonoid.toAddZeroClass
AddZeroClass.toAddZero
instAddZeroClass
Prod.instAddZeroClass
AddMonoidHom.instFunLike
toProd
inr
AddZero.toZero
β€”β€”
toProd_comp_inl πŸ“–mathematicalβ€”AddMonoidHom.comp
AddMonoid.Coprod
AddMonoid.toAddZeroClass
AddZeroClass.toAddZero
instAddZeroClass
Prod.instAddZeroClass
toProd
inl
AddMonoidHom.inl
β€”β€”
toProd_comp_inr πŸ“–mathematicalβ€”AddMonoidHom.comp
AddMonoid.Coprod
AddMonoid.toAddZeroClass
AddZeroClass.toAddZero
instAddZeroClass
Prod.instAddZeroClass
toProd
inr
AddMonoidHom.inr
β€”β€”
toProd_surjective πŸ“–mathematicalβ€”AddMonoid.Coprod
AddMonoid.toAddZeroClass
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
instAddZeroClass
Prod.instAddZeroClass
AddMonoidHom.instFunLike
toProd
β€”map_add
AddMonoidHomClass.toAddHomClass
AddMonoidHom.instAddMonoidHomClass
toProd_apply_inl
toProd_apply_inr
Prod.fst_add_snd

Monoid

Definitions

NameCategoryTheorems
Coprod πŸ“–CompOp
99 mathmath: Coprod.inl_injective, Coprod.fst_apply_inl, Coprod.swap_inr, Coprod.lift_apply_inr, Coprod.map_apply_inl, Coprod.con_ker_mk, Coprod.range_inl_sup_range_inr, Coprod.map_comp_inr, Coprod.map_comp_inl, Coprod.lift_inr_inl, Coprod.fst_toProd, Coprod.swap_surjective, Coprod.fst_comp_inr, Coprod.toProd_surjective, Coprod.clift_comp_mk, Coprod.map_map, Coprod.clift_apply_mk, Coprod.swap_injective, Coprod.mrange_swap, Coprod.closure_range_inl_union_inr, Coprod.mrange_eq, MulEquiv.coprodPUnit_symm_apply, MulEquiv.coprodAssoc_symm_apply_inr_inr, Coprod.map_apply_inr, Coprod.prod_mk_fst_snd, MulEquiv.coprodPUnit_apply, MulEquiv.coprodAssoc_apply_inl_inl, Coprod.toProd_apply_inr, Coprod.snd_comp_inr, Coprod.swap_comp_inr, Coprod.range_swap, Coprod.lift_apply_inl, Coprod.fst_comp_inl, MulEquiv.coprodAssoc_apply_inl_inr, Coprod.fst_apply_inr, Coprod.swap_map, MulEquiv.coprodCongr_apply, Coprod.snd_comp_toProd, Coprod.snd_swap, Coprod.mrange_lift, Coprod.range_lift, MulEquiv.coprodAssoc_apply_inr, Coprod.lift_inl_inr, Coprod.clift_apply_inr, MulEquiv.punitCoprod_symm_apply, MulEquiv.coprodComm_symm_apply, Coprod.comp_lift, Coprod.mk_of_inr, Coprod.lift_comp_swap, Coprod.mker_swap, Coprod.hom_ext_iff, Coprod.snd_comp_inl, Coprod.toProd_comp_inr, Coprod.clift_mk, Coprod.swap_comp_swap, Coprod.mrange_mk, MulEquiv.coprodComm_apply, Coprod.inv_def, Coprod.lift_comp_inr, Coprod.swap_eq_one, Coprod.snd_apply_inl, Coprod.lift_swap, Coprod.fst_swap, Coprod.snd_comp_swap, Coprod.mk_of_inl, Coprod.snd_toProd, MulEquiv.punitCoprod_apply, Coprod.lift_comp_inl, Coprod.toProd_comp_inl, MulEquiv.coprodCongr_symm_apply, Coprod.swap_bijective, Coprod.map_comp_map, Coprod.fst_comp_toProd, MulEquiv.coprodAssoc_symm_apply_inl, Coprod.fst_comp_swap, Coprod.mclosure_range_inl_union_inr, Coprod.clift_apply_inl, Coprod.range_eq, Coprod.mk_surjective, MulEquiv.coprodAssoc_symm_apply_inr_inl, Coprod.lift_apply_mk, Coprod.map_id_id, Coprod.codisjoint_range_inl_range_inr, Coprod.map_mk_ofList, Coprod.swap_swap, Coprod.fst_surjective, Coprod.fst_prod_snd, Coprod.toProd_apply_inl, Coprod.mrange_inl_sup_mrange_inr, Coprod.mk_of_inv_mul, Coprod.mk_eq_mk, Coprod.inr_injective, Coprod.codisjoint_mrange_inl_mrange_inr, Coprod.snd_apply_inr, Coprod.swap_comp_map, Coprod.swap_inj, Coprod.swap_inl, Coprod.snd_surjective, Coprod.swap_comp_inl
coprodCon πŸ“–CompOp
3 mathmath: Coprod.con_ker_mk, Coprod.con_inv_mul_cancel, Coprod.mk_eq_mk

Monoid.Coprod

Definitions

NameCategoryTheorems
clift πŸ“–CompOp
5 mathmath: clift_comp_mk, clift_apply_mk, clift_apply_inr, clift_mk, clift_apply_inl
fst πŸ“–CompOp
14 mathmath: fst_apply_inl, fst_toProd, fst_comp_inr, prod_mk_fst_snd, MulEquiv.coprodPUnit_apply, fst_comp_inl, fst_apply_inr, snd_swap, fst_swap, snd_comp_swap, fst_comp_toProd, fst_comp_swap, fst_surjective, fst_prod_snd
inl πŸ“–CompOp
34 mathmath: inl_injective, fst_apply_inl, swap_inr, map_apply_inl, range_inl_sup_range_inr, map_comp_inl, lift_inr_inl, closure_range_inl_union_inr, mrange_eq, MulEquiv.coprodPUnit_symm_apply, MulEquiv.coprodAssoc_apply_inl_inl, swap_comp_inr, lift_apply_inl, fst_comp_inl, MulEquiv.coprodAssoc_apply_inl_inr, lift_inl_inr, hom_ext_iff, snd_comp_inl, clift_mk, snd_apply_inl, mk_of_inl, lift_comp_inl, toProd_comp_inl, MulEquiv.coprodAssoc_symm_apply_inl, mclosure_range_inl_union_inr, clift_apply_inl, range_eq, MulEquiv.coprodAssoc_symm_apply_inr_inl, codisjoint_range_inl_range_inr, toProd_apply_inl, mrange_inl_sup_mrange_inr, codisjoint_mrange_inl_mrange_inr, swap_inl, swap_comp_inl
inr πŸ“–CompOp
34 mathmath: swap_inr, lift_apply_inr, range_inl_sup_range_inr, map_comp_inr, lift_inr_inl, fst_comp_inr, closure_range_inl_union_inr, mrange_eq, MulEquiv.coprodAssoc_symm_apply_inr_inr, map_apply_inr, toProd_apply_inr, snd_comp_inr, swap_comp_inr, MulEquiv.coprodAssoc_apply_inl_inr, fst_apply_inr, MulEquiv.coprodAssoc_apply_inr, lift_inl_inr, clift_apply_inr, MulEquiv.punitCoprod_symm_apply, mk_of_inr, hom_ext_iff, toProd_comp_inr, clift_mk, lift_comp_inr, mclosure_range_inl_union_inr, range_eq, MulEquiv.coprodAssoc_symm_apply_inr_inl, codisjoint_range_inl_range_inr, mrange_inl_sup_mrange_inr, inr_injective, codisjoint_mrange_inl_mrange_inr, snd_apply_inr, swap_inl, swap_comp_inl
inst πŸ“–CompOp
2 mathmath: lift_inr_inl, lift_inl_inr
instGroup πŸ“–CompOp
6 mathmath: range_inl_sup_range_inr, closure_range_inl_union_inr, range_swap, range_lift, range_eq, codisjoint_range_inl_range_inr
instInv πŸ“–CompOp
1 mathmath: inv_def
instMulOneClass πŸ“–CompOp
94 mathmath: inl_injective, fst_apply_inl, swap_inr, lift_apply_inr, map_apply_inl, con_ker_mk, map_comp_inr, map_comp_inl, fst_toProd, swap_surjective, fst_comp_inr, toProd_surjective, clift_comp_mk, map_map, clift_apply_mk, swap_injective, mrange_swap, closure_range_inl_union_inr, mrange_eq, MulEquiv.coprodPUnit_symm_apply, MulEquiv.coprodAssoc_symm_apply_inr_inr, map_apply_inr, prod_mk_fst_snd, MulEquiv.coprodPUnit_apply, MulEquiv.coprodAssoc_apply_inl_inl, toProd_apply_inr, snd_comp_inr, swap_comp_inr, lift_apply_inl, fst_comp_inl, MulEquiv.coprodAssoc_apply_inl_inr, fst_apply_inr, swap_map, MulEquiv.coprodCongr_apply, snd_comp_toProd, snd_swap, mrange_lift, MulEquiv.coprodAssoc_apply_inr, lift_inl_inr, clift_apply_inr, MulEquiv.punitCoprod_symm_apply, MulEquiv.coprodComm_symm_apply, comp_lift, mk_of_inr, lift_comp_swap, mker_swap, hom_ext_iff, snd_comp_inl, toProd_comp_inr, clift_mk, swap_comp_swap, mrange_mk, MulEquiv.coprodComm_apply, inv_def, lift_comp_inr, swap_eq_one, snd_apply_inl, lift_swap, fst_swap, snd_comp_swap, mk_of_inl, snd_toProd, MulEquiv.punitCoprod_apply, lift_comp_inl, toProd_comp_inl, MulEquiv.coprodCongr_symm_apply, swap_bijective, map_comp_map, fst_comp_toProd, MulEquiv.coprodAssoc_symm_apply_inl, fst_comp_swap, mclosure_range_inl_union_inr, clift_apply_inl, range_eq, mk_surjective, MulEquiv.coprodAssoc_symm_apply_inr_inl, lift_apply_mk, map_id_id, map_mk_ofList, swap_swap, fst_surjective, fst_prod_snd, toProd_apply_inl, mrange_inl_sup_mrange_inr, mk_of_inv_mul, mk_eq_mk, inr_injective, codisjoint_mrange_inl_mrange_inr, snd_apply_inr, swap_comp_map, swap_inj, swap_inl, snd_surjective, swap_comp_inl
liftEquiv πŸ“–CompOpβ€”
map πŸ“–CompOp
12 mathmath: map_apply_inl, map_comp_inr, map_comp_inl, map_map, map_apply_inr, swap_map, MulEquiv.coprodCongr_apply, MulEquiv.coprodCongr_symm_apply, map_comp_map, map_id_id, map_mk_ofList, swap_comp_map
mk πŸ“–CompOpβ€”
snd πŸ“–CompOp
14 mathmath: prod_mk_fst_snd, snd_comp_inr, snd_comp_toProd, snd_swap, snd_comp_inl, snd_apply_inl, fst_swap, snd_comp_swap, snd_toProd, MulEquiv.punitCoprod_apply, fst_comp_swap, fst_prod_snd, snd_apply_inr, snd_surjective
swap πŸ“–CompOp
25 mathmath: swap_inr, lift_inr_inl, swap_surjective, swap_injective, mrange_swap, swap_comp_inr, range_swap, swap_map, snd_swap, MulEquiv.coprodComm_symm_apply, lift_comp_swap, mker_swap, swap_comp_swap, MulEquiv.coprodComm_apply, swap_eq_one, lift_swap, fst_swap, snd_comp_swap, swap_bijective, fst_comp_swap, swap_swap, swap_comp_map, swap_inj, swap_inl, swap_comp_inl
toProd πŸ“–CompOp
11 mathmath: fst_toProd, toProd_surjective, prod_mk_fst_snd, toProd_apply_inr, snd_comp_toProd, toProd_comp_inr, snd_toProd, toProd_comp_inl, fst_comp_toProd, fst_prod_snd, toProd_apply_inl
Β«term_βˆ—_Β» πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
clift_apply_inl πŸ“–mathematicalDFunLike.coe
MonoidHom
FreeMonoid
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
FreeMonoid.instCancelMonoid
MonoidHom.instFunLike
FreeMonoid.of
MulOne.toOne
MulOne.toMul
Monoid.Coprod
instMulOneClass
clift
inl
β€”β€”
clift_apply_inr πŸ“–mathematicalDFunLike.coe
MonoidHom
FreeMonoid
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
FreeMonoid.instCancelMonoid
MonoidHom.instFunLike
FreeMonoid.of
MulOne.toOne
MulOne.toMul
Monoid.Coprod
instMulOneClass
clift
inr
β€”β€”
clift_apply_mk πŸ“–mathematicalDFunLike.coe
MonoidHom
FreeMonoid
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
FreeMonoid.instCancelMonoid
MonoidHom.instFunLike
FreeMonoid.of
MulOne.toOne
MulOne.toMul
Monoid.Coprod
instMulOneClass
clift
β€”β€”
clift_comp_mk πŸ“–mathematicalDFunLike.coe
MonoidHom
FreeMonoid
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
FreeMonoid.instCancelMonoid
MonoidHom.instFunLike
FreeMonoid.of
MulOne.toOne
MulOne.toMul
MonoidHom.comp
Monoid.Coprod
instMulOneClass
clift
β€”DFunLike.ext'
clift_mk πŸ“–mathematicalβ€”clift
Monoid.Coprod
instMulOneClass
map_one
MonoidHom
MulOneClass.toMulOne
MulOne.toOne
MonoidHom.instFunLike
MonoidHomClass.toOneHomClass
MonoidHom.instMonoidHomClass
inl
inr
map_mul
MulOne.toMul
MonoidHomClass.toMulHomClass
MonoidHom.id
β€”hom_ext
map_one
MonoidHomClass.toOneHomClass
MonoidHom.instMonoidHomClass
map_mul
MonoidHomClass.toMulHomClass
closure_range_inl_union_inr πŸ“–mathematicalβ€”Subgroup.closure
Monoid.Coprod
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instGroup
Set
Set.instUnion
Set.range
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
inl
inr
Top.top
Subgroup
Subgroup.instTop
β€”Subgroup.closure_eq_top_of_mclosure_eq_top
mclosure_range_inl_union_inr
codisjoint_mrange_inl_mrange_inr πŸ“–mathematicalβ€”Codisjoint
Submonoid
Monoid.Coprod
instMulOneClass
Submonoid.instPartialOrder
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
CompleteLattice.toBoundedOrder
Submonoid.instCompleteLattice
MonoidHom.mrange
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
inl
inr
β€”MonoidHom.instMonoidHomClass
codisjoint_iff
mrange_inl_sup_mrange_inr
codisjoint_range_inl_range_inr πŸ“–mathematicalβ€”Codisjoint
Subgroup
Monoid.Coprod
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instGroup
Subgroup.instPartialOrder
BoundedOrder.toOrderTop
Preorder.toLE
PartialOrder.toPreorder
CompleteLattice.toBoundedOrder
Subgroup.instCompleteLattice
MonoidHom.range
inl
inr
β€”codisjoint_iff
range_inl_sup_range_inr
comp_lift πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
Monoid.toMulOneClass
lift
β€”hom_ext
MonoidHom.comp_assoc
lift_comp_inl
lift_comp_inr
con_inv_mul_cancel πŸ“–mathematicalβ€”DFunLike.coe
Con
FreeMonoid
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
FreeMonoid.instCancelMonoid
Con.instFunLikeForallProp
Monoid.coprodCon
DivInvMonoid.toMonoid
Group.toDivInvMonoid
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
FreeMonoid.ofList
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
FreeMonoid.toList
MulOne.toOne
β€”map_mul
MonoidHomClass.toMulHomClass
MonoidHom.instMonoidHomClass
map_one
MonoidHomClass.toOneHomClass
FreeMonoid.inductionOn'
mul_one
mul_assoc
mk_of_inv_mul
one_mul
con_ker_mk πŸ“–mathematicalβ€”Con.ker
FreeMonoid
Monoid.Coprod
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
FreeMonoid.instCancelMonoid
instMulOneClass
MulOne.toMul
MonoidHom.instFunLike
MonoidHomClass.toMulHomClass
MonoidHom.instMonoidHomClass
Monoid.coprodCon
β€”Con.mk'_ker
fst_apply_inl πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
Monoid.toMulOneClass
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
fst
inl
β€”β€”
fst_apply_inr πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
Monoid.toMulOneClass
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
fst
inr
MulOne.toOne
β€”β€”
fst_comp_inl πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
Monoid.toMulOneClass
MulOneClass.toMulOne
instMulOneClass
fst
inl
MonoidHom.id
β€”β€”
fst_comp_inr πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
Monoid.toMulOneClass
MulOneClass.toMulOne
instMulOneClass
fst
inr
MonoidHom
instOneMonoidHom
β€”β€”
fst_comp_swap πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
Monoid.toMulOneClass
MulOneClass.toMulOne
instMulOneClass
fst
swap
snd
β€”lift_comp_swap
fst_comp_toProd πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
Monoid.toMulOneClass
MulOneClass.toMulOne
instMulOneClass
Prod.instMulOneClass
MonoidHom.fst
toProd
fst
β€”fst_prod_snd
MonoidHom.fst_comp_prod
fst_prod_snd πŸ“–mathematicalβ€”MonoidHom.prod
Monoid.Coprod
Monoid.toMulOneClass
instMulOneClass
fst
snd
toProd
β€”hom_ext
fst_surjective πŸ“–mathematicalβ€”Monoid.Coprod
Monoid.toMulOneClass
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
fst
β€”Function.LeftInverse.surjective
fst_apply_inl
fst_swap πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
Monoid.toMulOneClass
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
fst
swap
snd
β€”lift_swap
fst_toProd πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
Monoid.toMulOneClass
MulOneClass.toMulOne
instMulOneClass
Prod.instMulOneClass
MonoidHom.instFunLike
toProd
fst
β€”fst_comp_toProd
hom_ext πŸ“–β€”MonoidHom.comp
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
inl
inr
β€”β€”MonoidHom.eq_of_eqOn_denseM
mclosure_range_inl_union_inr
Set.eqOn_union
Set.eqOn_range
DFunLike.ext'_iff
hom_ext_iff πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
inl
inr
β€”hom_ext
induction_on πŸ“–β€”DFunLike.coe
MonoidHom
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
inl
inr
MulOne.toMul
β€”β€”induction_on'
map_one
MonoidHomClass.toOneHomClass
MonoidHom.instMonoidHomClass
induction_on' πŸ“–β€”Monoid.Coprod
MulOne.toOne
MulOneClass.toMulOne
instMulOneClass
MulOne.toMul
DFunLike.coe
MonoidHom
MonoidHom.instFunLike
inl
inr
β€”β€”mk_surjective
FreeMonoid.inductionOn'
map_mul
MonoidHomClass.toMulHomClass
MonoidHom.instMonoidHomClass
inl_injective πŸ“–mathematicalβ€”Monoid.Coprod
Monoid.toMulOneClass
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
inl
β€”fst_apply_inl
inr_injective πŸ“–mathematicalβ€”Monoid.Coprod
Monoid.toMulOneClass
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
inr
β€”snd_apply_inr
inv_def πŸ“–mathematicalβ€”Monoid.Coprod
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instInv
DFunLike.coe
MonoidHom
FreeMonoid
MulOneClass.toMulOne
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
FreeMonoid.instCancelMonoid
instMulOneClass
MonoidHom.instFunLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
FreeMonoid.ofList
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
FreeMonoid.toList
β€”β€”
lift_apply_inl πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
Monoid.toMulOneClass
MonoidHom.instFunLike
lift
inl
β€”β€”
lift_apply_inr πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
Monoid.toMulOneClass
MonoidHom.instFunLike
lift
inr
β€”β€”
lift_apply_mk πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
Monoid.toMulOneClass
MonoidHom.instFunLike
lift
FreeMonoid
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
FreeMonoid.instCancelMonoid
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
FreeMonoid.lift
β€”β€”
lift_comp_inl πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
Monoid.toMulOneClass
lift
inl
β€”β€”
lift_comp_inr πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
Monoid.toMulOneClass
lift
inr
β€”β€”
lift_comp_swap πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
Monoid.toMulOneClass
lift
swap
β€”hom_ext
lift_inl_inr πŸ“–mathematicalβ€”lift
Monoid.Coprod
Monoid.toMulOneClass
inst
inl
inr
MonoidHom.id
MulOneClass.toMulOne
instMulOneClass
β€”hom_ext
lift_inr_inl πŸ“–mathematicalβ€”lift
Monoid.Coprod
Monoid.toMulOneClass
inst
inr
inl
swap
β€”hom_ext
lift_swap πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
Monoid.toMulOneClass
MonoidHom.instFunLike
lift
swap
β€”DFunLike.congr_fun
lift_comp_swap
lift_unique πŸ“–mathematicalMonoidHom.comp
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
Monoid.toMulOneClass
inl
inr
liftβ€”hom_ext
map_apply_inl πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
map
inl
β€”β€”
map_apply_inr πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
map
inr
β€”β€”
map_comp_inl πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
map
inl
β€”β€”
map_comp_inr πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
map
inr
β€”β€”
map_comp_map πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
map
β€”hom_ext
map_id_id πŸ“–mathematicalβ€”map
MonoidHom.id
MulOneClass.toMulOne
Monoid.Coprod
instMulOneClass
β€”hom_ext
map_map πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
map
MonoidHom.comp
β€”DFunLike.congr_fun
map_comp_map
map_mk_ofList πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
map
FreeMonoid
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
FreeMonoid.instCancelMonoid
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
FreeMonoid.ofList
β€”β€”
mclosure_range_inl_union_inr πŸ“–mathematicalβ€”Submonoid.closure
Monoid.Coprod
instMulOneClass
Set
Set.instUnion
Set.range
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
inl
inr
Top.top
Submonoid
Submonoid.instTop
β€”MonoidHom.instMonoidHomClass
MonoidHom.mrange_eq_map
FreeMonoid.closure_range_of
MonoidHom.map_mclosure
Set.range_comp
Sum.range_eq
mk_eq_mk πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
FreeMonoid
Monoid.Coprod
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
FreeMonoid.instCancelMonoid
instMulOneClass
MonoidHom.instFunLike
Con
MulOne.toMul
Con.instFunLikeForallProp
Monoid.coprodCon
β€”Con.eq
mk_of_inl πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
FreeMonoid
Monoid.Coprod
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
FreeMonoid.instCancelMonoid
instMulOneClass
MonoidHom.instFunLike
FreeMonoid.of
inl
β€”β€”
mk_of_inr πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
FreeMonoid
Monoid.Coprod
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
FreeMonoid.instCancelMonoid
instMulOneClass
MonoidHom.instFunLike
FreeMonoid.of
inr
β€”β€”
mk_of_inv_mul πŸ“–mathematicalβ€”Monoid.Coprod
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MulOne.toMul
MulOneClass.toMulOne
instMulOneClass
DFunLike.coe
MonoidHom
FreeMonoid
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
FreeMonoid.instCancelMonoid
MonoidHom.instFunLike
FreeMonoid.of
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
MulOne.toOne
β€”map_mul_eq_one
MonoidHom.instMonoidHomClass
inv_mul_cancel
mk_surjective πŸ“–mathematicalβ€”FreeMonoid
Monoid.Coprod
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
FreeMonoid.instCancelMonoid
instMulOneClass
MonoidHom.instFunLike
β€”Quot.mk_surjective
mker_swap πŸ“–mathematicalβ€”MonoidHom.mker
Monoid.Coprod
instMulOneClass
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
swap
Bot.bot
Submonoid
Submonoid.instBot
β€”Submonoid.ext
MonoidHom.instMonoidHomClass
swap_eq_one
mrange_eq πŸ“–mathematicalβ€”MonoidHom.mrange
Monoid.Coprod
instMulOneClass
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
Submonoid
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
Submonoid.instCompleteLattice
MonoidHom.comp
inl
inr
β€”MonoidHom.instMonoidHomClass
MonoidHom.mrange_eq_map
mrange_inl_sup_mrange_inr
Submonoid.map_sup
MonoidHom.map_mrange
mrange_inl_sup_mrange_inr πŸ“–mathematicalβ€”Submonoid
Monoid.Coprod
instMulOneClass
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
Submonoid.instCompleteLattice
MonoidHom.mrange
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
inl
inr
Top.top
Submonoid.instTop
β€”MonoidHom.instMonoidHomClass
mclosure_range_inl_union_inr
Submonoid.closure_union
MonoidHom.coe_mrange
Submonoid.closure_eq
mrange_lift πŸ“–mathematicalβ€”MonoidHom.mrange
Monoid.Coprod
instMulOneClass
Monoid.toMulOneClass
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
lift
Submonoid
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
Submonoid.instCompleteLattice
β€”MonoidHom.instMonoidHomClass
mrange_eq
mrange_mk πŸ“–mathematicalβ€”MonoidHom.mrange
FreeMonoid
Monoid.Coprod
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
FreeMonoid.instCancelMonoid
instMulOneClass
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
Top.top
Submonoid
Submonoid.instTop
β€”Con.mrange_mk'
mrange_swap πŸ“–mathematicalβ€”MonoidHom.mrange
Monoid.Coprod
instMulOneClass
MonoidHom
MulOneClass.toMulOne
MonoidHom.instFunLike
MonoidHom.instMonoidHomClass
swap
Top.top
Submonoid
Submonoid.instTop
β€”MonoidHom.mrange_eq_top_of_surjective
MonoidHom.instMonoidHomClass
swap_surjective
prod_mk_fst_snd πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
Monoid.toMulOneClass
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
fst
snd
Prod.instMulOneClass
toProd
β€”fst_prod_snd
MonoidHom.prod_apply
range_eq πŸ“–mathematicalβ€”MonoidHom.range
Monoid.Coprod
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instGroup
Subgroup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
Subgroup.instCompleteLattice
MonoidHom.comp
MulOneClass.toMulOne
instMulOneClass
inl
inr
β€”MonoidHom.range_eq_map
range_inl_sup_range_inr
Subgroup.map_sup
MonoidHom.map_range
range_inl_sup_range_inr πŸ“–mathematicalβ€”Subgroup
Monoid.Coprod
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instGroup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
Subgroup.instCompleteLattice
MonoidHom.range
inl
inr
Top.top
Subgroup.instTop
β€”closure_range_inl_union_inr
Subgroup.closure_union
MonoidHom.coe_range
Subgroup.closure_eq
range_lift πŸ“–mathematicalβ€”MonoidHom.range
Monoid.Coprod
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instGroup
lift
Subgroup
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
Subgroup.instCompleteLattice
β€”range_eq
range_swap πŸ“–mathematicalβ€”MonoidHom.range
Monoid.Coprod
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instGroup
swap
Top.top
Subgroup
Subgroup.instTop
β€”MonoidHom.range_eq_top
swap_surjective
snd_apply_inl πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
Monoid.toMulOneClass
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
snd
inl
MulOne.toOne
β€”β€”
snd_apply_inr πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
Monoid.toMulOneClass
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
snd
inr
β€”β€”
snd_comp_inl πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
Monoid.toMulOneClass
MulOneClass.toMulOne
instMulOneClass
snd
inl
MonoidHom
instOneMonoidHom
β€”β€”
snd_comp_inr πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
Monoid.toMulOneClass
MulOneClass.toMulOne
instMulOneClass
snd
inr
MonoidHom.id
β€”β€”
snd_comp_swap πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
Monoid.toMulOneClass
MulOneClass.toMulOne
instMulOneClass
snd
swap
fst
β€”lift_comp_swap
snd_comp_toProd πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
Monoid.toMulOneClass
MulOneClass.toMulOne
instMulOneClass
Prod.instMulOneClass
MonoidHom.snd
toProd
snd
β€”fst_prod_snd
MonoidHom.snd_comp_prod
snd_surjective πŸ“–mathematicalβ€”Monoid.Coprod
Monoid.toMulOneClass
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
snd
β€”Function.LeftInverse.surjective
snd_apply_inr
snd_swap πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
Monoid.toMulOneClass
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
snd
swap
fst
β€”lift_swap
snd_toProd πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
Monoid.toMulOneClass
MulOneClass.toMulOne
instMulOneClass
Prod.instMulOneClass
MonoidHom.instFunLike
toProd
snd
β€”snd_comp_toProd
swap_bijective πŸ“–mathematicalβ€”Function.Bijective
Monoid.Coprod
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
swap
β€”swap_injective
swap_surjective
swap_comp_inl πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
swap
inl
inr
β€”β€”
swap_comp_inr πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
swap
inr
inl
β€”β€”
swap_comp_map πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
swap
map
β€”hom_ext
swap_comp_swap πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
swap
MonoidHom.id
β€”hom_ext
swap_eq_one πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
swap
MulOne.toOne
β€”swap_injective
map_one
MonoidHomClass.toOneHomClass
MonoidHom.instMonoidHomClass
swap_inj πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
swap
β€”swap_injective
swap_injective πŸ“–mathematicalβ€”Monoid.Coprod
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
swap
β€”swap_swap
swap_inl πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
swap
inl
inr
β€”β€”
swap_inr πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
swap
inr
inl
β€”β€”
swap_map πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
swap
map
β€”DFunLike.congr_fun
swap_comp_map
swap_surjective πŸ“–mathematicalβ€”Monoid.Coprod
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
swap
β€”Function.LeftInverse.surjective
swap_swap
swap_swap πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
MulOneClass.toMulOne
instMulOneClass
MonoidHom.instFunLike
swap
β€”DFunLike.congr_fun
swap_comp_swap
toProd_apply_inl πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
Monoid.toMulOneClass
MulOneClass.toMulOne
instMulOneClass
Prod.instMulOneClass
MonoidHom.instFunLike
toProd
inl
MulOne.toOne
β€”β€”
toProd_apply_inr πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Monoid.Coprod
Monoid.toMulOneClass
MulOneClass.toMulOne
instMulOneClass
Prod.instMulOneClass
MonoidHom.instFunLike
toProd
inr
MulOne.toOne
β€”β€”
toProd_comp_inl πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
Monoid.toMulOneClass
MulOneClass.toMulOne
instMulOneClass
Prod.instMulOneClass
toProd
inl
MonoidHom.inl
β€”β€”
toProd_comp_inr πŸ“–mathematicalβ€”MonoidHom.comp
Monoid.Coprod
Monoid.toMulOneClass
MulOneClass.toMulOne
instMulOneClass
Prod.instMulOneClass
toProd
inr
MonoidHom.inr
β€”β€”
toProd_surjective πŸ“–mathematicalβ€”Monoid.Coprod
Monoid.toMulOneClass
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
instMulOneClass
Prod.instMulOneClass
MonoidHom.instFunLike
toProd
β€”map_mul
MonoidHomClass.toMulHomClass
MonoidHom.instMonoidHomClass
toProd_apply_inl
toProd_apply_inr
Prod.fst_mul_snd

MulEquiv

Definitions

NameCategoryTheorems
coprodAssoc πŸ“–CompOp
6 mathmath: coprodAssoc_symm_apply_inr_inr, coprodAssoc_apply_inl_inl, coprodAssoc_apply_inl_inr, coprodAssoc_apply_inr, coprodAssoc_symm_apply_inl, coprodAssoc_symm_apply_inr_inl
coprodComm πŸ“–CompOp
2 mathmath: coprodComm_symm_apply, coprodComm_apply
coprodCongr πŸ“–CompOp
2 mathmath: coprodCongr_apply, coprodCongr_symm_apply
coprodPUnit πŸ“–CompOp
2 mathmath: coprodPUnit_symm_apply, coprodPUnit_apply
punitCoprod πŸ“–CompOp
2 mathmath: punitCoprod_symm_apply, punitCoprod_apply

Theorems

NameKindAssumesProvesValidatesDepends On
coprodAssoc_apply_inl_inl πŸ“–mathematicalβ€”DFunLike.coe
MulEquiv
Monoid.Coprod
Monoid.toMulOneClass
Monoid.Coprod.instMulOneClass
MulOne.toMul
MulOneClass.toMulOne
EquivLike.toFunLike
instEquivLike
coprodAssoc
MonoidHom
MonoidHom.instFunLike
Monoid.Coprod.inl
β€”β€”
coprodAssoc_apply_inl_inr πŸ“–mathematicalβ€”DFunLike.coe
MulEquiv
Monoid.Coprod
Monoid.toMulOneClass
Monoid.Coprod.instMulOneClass
MulOne.toMul
MulOneClass.toMulOne
EquivLike.toFunLike
instEquivLike
coprodAssoc
MonoidHom
MonoidHom.instFunLike
Monoid.Coprod.inl
Monoid.Coprod.inr
β€”β€”
coprodAssoc_apply_inr πŸ“–mathematicalβ€”DFunLike.coe
MulEquiv
Monoid.Coprod
Monoid.toMulOneClass
Monoid.Coprod.instMulOneClass
MulOne.toMul
MulOneClass.toMulOne
EquivLike.toFunLike
instEquivLike
coprodAssoc
MonoidHom
MonoidHom.instFunLike
Monoid.Coprod.inr
β€”β€”
coprodAssoc_symm_apply_inl πŸ“–mathematicalβ€”DFunLike.coe
MulEquiv
Monoid.Coprod
Monoid.toMulOneClass
Monoid.Coprod.instMulOneClass
MulOne.toMul
MulOneClass.toMulOne
EquivLike.toFunLike
instEquivLike
symm
coprodAssoc
MonoidHom
MonoidHom.instFunLike
Monoid.Coprod.inl
β€”β€”
coprodAssoc_symm_apply_inr_inl πŸ“–mathematicalβ€”DFunLike.coe
MulEquiv
Monoid.Coprod
Monoid.toMulOneClass
Monoid.Coprod.instMulOneClass
MulOne.toMul
MulOneClass.toMulOne
EquivLike.toFunLike
instEquivLike
symm
coprodAssoc
MonoidHom
MonoidHom.instFunLike
Monoid.Coprod.inr
Monoid.Coprod.inl
β€”β€”
coprodAssoc_symm_apply_inr_inr πŸ“–mathematicalβ€”DFunLike.coe
MulEquiv
Monoid.Coprod
Monoid.toMulOneClass
Monoid.Coprod.instMulOneClass
MulOne.toMul
MulOneClass.toMulOne
EquivLike.toFunLike
instEquivLike
symm
coprodAssoc
MonoidHom
MonoidHom.instFunLike
Monoid.Coprod.inr
β€”β€”
coprodComm_apply πŸ“–mathematicalβ€”DFunLike.coe
MulEquiv
Monoid.Coprod
MulOne.toMul
MulOneClass.toMulOne
Monoid.Coprod.instMulOneClass
EquivLike.toFunLike
instEquivLike
coprodComm
MonoidHom
MonoidHom.instFunLike
Monoid.Coprod.swap
β€”β€”
coprodComm_symm_apply πŸ“–mathematicalβ€”DFunLike.coe
MulEquiv
Monoid.Coprod
MulOne.toMul
MulOneClass.toMulOne
Monoid.Coprod.instMulOneClass
EquivLike.toFunLike
instEquivLike
symm
coprodComm
MonoidHom
MonoidHom.instFunLike
Monoid.Coprod.swap
β€”β€”
coprodCongr_apply πŸ“–mathematicalβ€”DFunLike.coe
MulEquiv
Monoid.Coprod
MulOne.toMul
MulOneClass.toMulOne
Monoid.Coprod.instMulOneClass
EquivLike.toFunLike
instEquivLike
coprodCongr
MonoidHom
MonoidHom.instFunLike
Monoid.Coprod.map
MonoidHomClass.toMonoidHom
β€”β€”
coprodCongr_symm_apply πŸ“–mathematicalβ€”DFunLike.coe
MulEquiv
Monoid.Coprod
MulOne.toMul
MulOneClass.toMulOne
Monoid.Coprod.instMulOneClass
EquivLike.toFunLike
instEquivLike
symm
coprodCongr
MonoidHom
MonoidHom.instFunLike
Monoid.Coprod.map
MonoidHomClass.toMonoidHom
β€”β€”
coprodPUnit_apply πŸ“–mathematicalβ€”DFunLike.coe
MulEquiv
Monoid.Coprod
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
PUnit.commGroup
MulOne.toMul
MulOneClass.toMulOne
Monoid.Coprod.instMulOneClass
EquivLike.toFunLike
instEquivLike
coprodPUnit
MonoidHom
MonoidHom.instFunLike
Monoid.Coprod.fst
β€”β€”
coprodPUnit_symm_apply πŸ“–mathematicalβ€”DFunLike.coe
MulEquiv
Monoid.Coprod
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
PUnit.commGroup
MulOne.toMul
MulOneClass.toMulOne
Monoid.Coprod.instMulOneClass
EquivLike.toFunLike
instEquivLike
symm
coprodPUnit
MonoidHom
MonoidHom.instFunLike
Monoid.Coprod.inl
β€”β€”
punitCoprod_apply πŸ“–mathematicalβ€”DFunLike.coe
MulEquiv
Monoid.Coprod
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
PUnit.commGroup
MulOne.toMul
MulOneClass.toMulOne
Monoid.Coprod.instMulOneClass
EquivLike.toFunLike
instEquivLike
punitCoprod
MonoidHom
MonoidHom.instFunLike
Monoid.Coprod.snd
β€”β€”
punitCoprod_symm_apply πŸ“–mathematicalβ€”DFunLike.coe
MulEquiv
Monoid.Coprod
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
PUnit.commGroup
MulOne.toMul
MulOneClass.toMulOne
Monoid.Coprod.instMulOneClass
EquivLike.toFunLike
instEquivLike
symm
punitCoprod
MonoidHom
MonoidHom.instFunLike
Monoid.Coprod.inr
β€”β€”

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