Documentation Verification Report

Basic

📁 Source: Mathlib/Algebra/FreeMonoid/Basic.lean

Statistics

MetricCount
DefinitionsFreeAddMonoid, casesOn, freeAddMonoidCongr, instAddCancelMonoid, instInhabited, instMembership, instUniqueOfIsEmpty, length, map, mem, mkAddAction, of, ofList, recOn, reverse, sumAux, toList, uniqueAddUnits, FreeMonoid, casesOn, freeMonoidCongr, instCancelMonoid, instInhabited, instMembership, instUniqueOfIsEmpty, length, map, mem, mkMulAction, of, ofList, prodAux, recOn, reverse, toList, uniqueUnits
36
TheoremscasesOn_of_add, casesOn_zero, comp_lift, freeAddMonoidCongr_of, freeAddMonoidCongr_symm_of, hom_eq, hom_eq_iff, hom_map_lift, inductionOn, inductionOn', length_add, length_eq_four, length_eq_one, length_eq_three, length_eq_two, length_eq_zero, length_of, length_reverse, length_zero, lift_apply, lift_comp_of, lift_eval_of, lift_ofList, lift_of_comp_eq_map, lift_restrict, lift_symm_apply, map_apply_map_symm_eq, map_comp, map_id, map_map, map_of, map_surjective, map_symm_apply_map_eq, mem_add, mem_map, mem_of, mem_of_self, notMem_zero, ofList_append, ofList_comp_toList, ofList_cons, ofList_flatten, ofList_map, ofList_nil, ofList_singleton, ofList_symm, ofList_toList, ofList_vadd, of_injective, of_ne_zero, of_vadd, recOn_of_add, recOn_zero, reverse_add, reverse_of, reverse_reverse, sumAux_eq, toList_add, toList_comp_ofList, toList_cons, toList_map, toList_nil, toList_of, toList_ofList, toList_of_add, toList_sum, toList_symm, toList_zero, vadd_def, zero_ne_of, casesOn_of_mul, casesOn_one, comp_lift, freeMonoidCongr_of, freeMonoidCongr_symm_of, hom_eq, hom_eq_iff, hom_map_lift, inductionOn, inductionOn', length_eq_four, length_eq_one, length_eq_three, length_eq_two, length_eq_zero, length_mul, length_of, length_one, length_reverse, lift_apply, lift_comp_of, lift_eval_of, lift_ofList, lift_of_comp_eq_map, lift_restrict, lift_symm_apply, map_apply_map_symm_eq, map_comp, map_id, map_map, map_of, map_surjective, map_symm_apply_map_eq, mem_map, mem_mul, mem_of, mem_of_self, notMem_one, ofList_append, ofList_comp_toList, ofList_cons, ofList_flatten, ofList_map, ofList_nil, ofList_singleton, ofList_smul, ofList_symm, ofList_toList, of_injective, of_ne_one, of_smul, one_ne_of, prodAux_eq, recOn_of_mul, recOn_one, reverse_mul, reverse_of, reverse_reverse, smul_def, toList_comp_ofList, toList_cons, toList_map, toList_mul, toList_nil, toList_of, toList_ofList, toList_of_mul, toList_one, toList_prod, toList_symm
140
Total176

FreeAddMonoid

Definitions

NameCategoryTheorems
casesOn 📖CompOp
freeAddMonoidCongr 📖CompOp
2 mathmath: freeAddMonoidCongr_of, freeAddMonoidCongr_symm_of
instAddCancelMonoid 📖CompOp
79 mathmath: lift_symm_apply, casesOn_zero, length_zero, length_eq_zero, toList_sum, lift_ofList, count_apply, AddMonoid.Coprod.mk_of_inr, toPiTensorProduct, lift_apply, length_add, PresentedAddMonoid.surjective_mk, count_of, PiTensorProduct.lifts_smul, PiTensorProduct.projectiveSeminormAux_smul, mem_add, AddMonoid.Coprod.neg_def, vadd_def, mem_map, map_comp, PiTensorProduct.lifts_add, recOn_of_add, ofList_append, ofList_vadd, ofList_map, map_surjective, toList_zero, ofList_cons, reverse_add, toList_add, PiTensorProduct.lifts_zero, notMem_zero, ofList_nil, toList_map, freeAddMonoidCongr_of, AddMonoid.Coprod.mk_surjective, AddMonoid.Coprod.mk_of_neg_add, toList_of_add, countP'_add, AddMonoid.fg_iff_exists_freeAddMonoid_hom_surjective, map_id, lift_comp_of, freeAddMonoidCongr_symm_of, closure_range_of, AddMonoid.Coprod.map_mk_ofList, AddMonoid.Coprod.mk_eq_mk, casesOn_of_add, TensorProduct.SMul.aux_of, symbols_zero, lift_eval_of, mrange_lift, recOn_zero, lift_restrict, length_eq_three, AddMonoid.Coprod.lift_apply_mk, AddMonoid.Coprod.mrange_mk, instTwoUniqueSums, length_eq_two, map_symm_apply_map_eq, countP'_zero, comp_lift, ofList_flatten, lift_of_comp_eq_map, map_of, map_apply_map_symm_eq, AddMonoid.Coprod.con_ker_mk, countP_apply, of_vadd, symbols_add, hom_map_lift, map_map, countP_of, CharacterModule.homEquiv_apply_apply, AddSubmonoid.closure_eq_mrange, AddMonoid.Coprod.mk_of_inl, hom_eq_iff, length_eq_four, AddMonoid.Coprod.con_neg_add_cancel, PiTensorProduct.projectiveSeminormAux_add_le
instInhabited 📖CompOp
instMembership 📖CompOp
6 mathmath: mem_add, mem_map, mem_of, mem_of_self, notMem_zero, mem_symbols
instUniqueOfIsEmpty 📖CompOp
length 📖CompOp
9 mathmath: length_zero, length_eq_zero, length_add, length_reverse, length_eq_three, length_eq_one, length_eq_two, length_of, length_eq_four
map 📖CompOp
13 mathmath: PiTensorProduct.lifts_smul, PiTensorProduct.projectiveSeminormAux_smul, mem_map, map_comp, ofList_map, map_surjective, toList_map, map_id, map_symm_apply_map_eq, lift_of_comp_eq_map, map_of, map_apply_map_symm_eq, map_map
mem 📖MathDef
mkAddAction 📖CompOp
3 mathmath: vadd_def, ofList_vadd, of_vadd
of 📖CompOp
33 mathmath: lift_symm_apply, AddMonoid.Coprod.mk_of_inr, count_of, recOn_of_add, mem_of, mem_of_self, toList_of, ofList_cons, freeAddMonoidCongr_of, AddMonoid.Coprod.mk_of_neg_add, reverse_of, toList_of_add, lift_comp_of, freeAddMonoidCongr_symm_of, symbols_of, closure_range_of, casesOn_of_add, TensorProduct.SMul.aux_of, lift_eval_of, lift_restrict, length_eq_three, length_eq_one, length_eq_two, lift_of_comp_eq_map, map_of, length_of, of_vadd, countP_of, AddMonoid.Coprod.mk_of_inl, ofList_singleton, hom_eq_iff, of_injective, length_eq_four
ofList 📖CompOp
17 mathmath: lift_ofList, toList_comp_ofList, AddMonoid.Coprod.neg_def, ofList_append, ofList_vadd, ofList_map, ofList_cons, ofList_nil, ofList_symm, ofList_toList, AddMonoid.Coprod.map_mk_ofList, ofList_flatten, toList_ofList, toList_symm, ofList_comp_toList, ofList_singleton, AddMonoid.Coprod.con_neg_add_cancel
recOn 📖CompOp
reverse 📖CompOp
4 mathmath: reverse_add, length_reverse, reverse_of, reverse_reverse
sumAux 📖CompOp
1 mathmath: sumAux_eq
toList 📖CompOp
23 mathmath: toList_sum, count_apply, toPiTensorProduct, lift_apply, toList_comp_ofList, AddMonoid.Coprod.neg_def, vadd_def, toList_of, toList_zero, toList_add, toList_map, ofList_symm, ofList_toList, toList_of_add, PiTensorProduct.mem_lifts_iff, toList_ofList, toList_symm, countP_apply, ofList_comp_toList, FreeMonoid.count_apply, toList_cons, toList_nil, AddMonoid.Coprod.con_neg_add_cancel
uniqueAddUnits 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
casesOn_of_add 📖mathematicalFreeAddMonoid
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
of
casesOn_zero 📖mathematicalFreeAddMonoid
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
comp_lift 📖mathematicalAddMonoidHom.comp
FreeAddMonoid
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
DFunLike.coe
Equiv
AddMonoidHom
EquivLike.toFunLike
Equiv.instEquivLike
lift
AddMonoidHom.instFunLike
hom_eq
freeAddMonoidCongr_of 📖mathematicalDFunLike.coe
AddEquiv
FreeAddMonoid
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
EquivLike.toFunLike
AddEquiv.instEquivLike
freeAddMonoidCongr
of
Equiv
Equiv.instEquivLike
freeAddMonoidCongr_symm_of 📖mathematicalDFunLike.coe
AddEquiv
FreeAddMonoid
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
EquivLike.toFunLike
AddEquiv.instEquivLike
freeAddMonoidCongr
Equiv.symm
of
Equiv
Equiv.instEquivLike
hom_eq 📖DFunLike.coe
AddMonoidHom
FreeAddMonoid
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
AddMonoidHom.instFunLike
of
AddMonoidHom.ext
AddMonoidHom.map_zero
map_add
AddMonoidHomClass.toAddHomClass
AddMonoidHom.instAddMonoidHomClass
hom_eq_iff 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddMonoid
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
AddMonoidHom.instFunLike
of
hom_eq
hom_map_lift 📖mathematicalDFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddMonoidHom.instFunLike
FreeAddMonoid
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
DFunLike.ext_iff
comp_lift
inductionOn 📖FreeAddMonoid
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
of
AddZero.toAdd
inductionOn' 📖FreeAddMonoid
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
AddZero.toAdd
of
length_add 📖mathematicallength
FreeAddMonoid
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
length_eq_four 📖mathematicallength
FreeAddMonoid
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
of
List.length_eq_four
length_eq_one 📖mathematicallength
of
length_eq_three 📖mathematicallength
FreeAddMonoid
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
of
List.length_eq_three
length_eq_two 📖mathematicallength
FreeAddMonoid
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
of
List.length_eq_two
length_eq_zero 📖mathematicallength
FreeAddMonoid
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
length_of 📖mathematicallength
of
length_reverse 📖mathematicallength
reverse
length_zero 📖mathematicallength
FreeAddMonoid
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
lift_apply 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddMonoid
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
AddMonoidHom.instFunLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
AddZero.toAdd
AddZero.toZero
toList
sumAux_eq
lift_comp_of 📖mathematicalFreeAddMonoid
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
AddMonoidHom.instFunLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
lift_eval_of 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddMonoid
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
AddMonoidHom.instFunLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
lift_ofList 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddMonoid
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
AddMonoidHom.instFunLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
ofList
AddZero.toAdd
AddZero.toZero
sumAux_eq
lift_of_comp_eq_map 📖mathematicalDFunLike.coe
Equiv
AddMonoidHom
FreeAddMonoid
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
map
hom_eq
lift_restrict 📖mathematicalDFunLike.coe
Equiv
AddMonoidHom
FreeAddMonoid
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
EquivLike.toFunLike
Equiv.instEquivLike
lift
AddMonoidHom.instFunLike
of
Equiv.apply_symm_apply
lift_symm_apply 📖mathematicalDFunLike.coe
Equiv
AddMonoidHom
FreeAddMonoid
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
lift
AddMonoidHom.instFunLike
of
map_apply_map_symm_eq 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddMonoid
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
AddMonoidHom.instFunLike
map
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
map_map
Equiv.self_comp_symm
map_id
map_comp 📖mathematicalmap
AddMonoidHom.comp
FreeAddMonoid
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
hom_eq
map_id 📖mathematicalmap
AddMonoidHom.id
FreeAddMonoid
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
hom_eq
map_map 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddMonoid
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
AddMonoidHom.instFunLike
map
map_of 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddMonoid
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
AddMonoidHom.instFunLike
map
of
map_surjective 📖mathematicalFreeAddMonoid
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
AddMonoidHom.instFunLike
map
inductionOn'
map_zero
AddMonoidHomClass.toZeroHomClass
AddMonoidHom.instAddMonoidHomClass
map_add
AddMonoidHomClass.toAddHomClass
of_injective
add_zero
length_add
add_eq_left
AddLeftCancelSemigroup.toIsLeftCancelAdd
length_eq_zero
map_symm_apply_map_eq 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddMonoid
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
AddMonoidHom.instFunLike
map
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
map_map
Equiv.symm_comp_self
map_id
mem_add 📖mathematicalFreeAddMonoid
instMembership
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
mem_map 📖mathematicalFreeAddMonoid
instMembership
DFunLike.coe
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
AddMonoidHom.instFunLike
map
mem_of 📖mathematicalFreeAddMonoid
instMembership
of
mem_of_self 📖mathematicalFreeAddMonoid
instMembership
of
notMem_zero 📖mathematicalFreeAddMonoid
instMembership
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
ofList_append 📖mathematicalDFunLike.coe
Equiv
FreeAddMonoid
EquivLike.toFunLike
Equiv.instEquivLike
ofList
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
ofList_comp_toList 📖mathematicalFreeAddMonoid
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
ofList
toList
ofList_cons 📖mathematicalDFunLike.coe
Equiv
FreeAddMonoid
EquivLike.toFunLike
Equiv.instEquivLike
ofList
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
of
ofList_flatten 📖mathematicalDFunLike.coe
Equiv
FreeAddMonoid
EquivLike.toFunLike
Equiv.instEquivLike
ofList
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
AddZero.toZero
Equiv.injective
toList_sum
ofList_map 📖mathematicalDFunLike.coe
Equiv
FreeAddMonoid
EquivLike.toFunLike
Equiv.instEquivLike
ofList
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
AddMonoidHom.instFunLike
map
ofList_nil 📖mathematicalDFunLike.coe
Equiv
FreeAddMonoid
EquivLike.toFunLike
Equiv.instEquivLike
ofList
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
ofList_singleton 📖mathematicalDFunLike.coe
Equiv
FreeAddMonoid
EquivLike.toFunLike
Equiv.instEquivLike
ofList
of
ofList_symm 📖mathematicalEquiv.symm
FreeAddMonoid
ofList
toList
ofList_toList 📖mathematicalDFunLike.coe
Equiv
FreeAddMonoid
EquivLike.toFunLike
Equiv.instEquivLike
ofList
toList
ofList_vadd 📖mathematicalHVAdd.hVAdd
FreeAddMonoid
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
AddAction.toAddSemigroupAction
mkAddAction
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
ofList
of_injective 📖mathematicalFreeAddMonoid
of
List.singleton_injective
of_ne_zero 📖
of_vadd 📖mathematicalHVAdd.hVAdd
FreeAddMonoid
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
AddAction.toAddSemigroupAction
mkAddAction
of
recOn_of_add 📖mathematicalFreeAddMonoid
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
of
recOn_zero 📖mathematicalFreeAddMonoid
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
reverse_add 📖mathematicalreverse
FreeAddMonoid
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
reverse_of 📖mathematicalreverse
of
reverse_reverse 📖mathematicalreverse
sumAux_eq 📖mathematicalsumAux
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddZero.toZero
AddSemigroup.to_isAssociative
AddSemigroup.to_isLawfulIdentity
zero_add
toList_add 📖mathematicalDFunLike.coe
Equiv
FreeAddMonoid
EquivLike.toFunLike
Equiv.instEquivLike
toList
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
toList_comp_ofList 📖mathematicalFreeAddMonoid
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
toList
ofList
toList_cons 📖mathematicalDFunLike.coe
Equiv
FreeAddMonoid
EquivLike.toFunLike
Equiv.instEquivLike
toList
toList_map 📖mathematicalDFunLike.coe
Equiv
FreeAddMonoid
EquivLike.toFunLike
Equiv.instEquivLike
toList
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
AddMonoidHom.instFunLike
map
toList_nil 📖mathematicalDFunLike.coe
Equiv
FreeAddMonoid
EquivLike.toFunLike
Equiv.instEquivLike
toList
toList_of 📖mathematicalDFunLike.coe
Equiv
FreeAddMonoid
EquivLike.toFunLike
Equiv.instEquivLike
toList
of
toList_ofList 📖mathematicalDFunLike.coe
Equiv
FreeAddMonoid
EquivLike.toFunLike
Equiv.instEquivLike
toList
ofList
toList_of_add 📖mathematicalDFunLike.coe
Equiv
FreeAddMonoid
EquivLike.toFunLike
Equiv.instEquivLike
toList
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
of
toList_sum 📖mathematicalDFunLike.coe
Equiv
FreeAddMonoid
EquivLike.toFunLike
Equiv.instEquivLike
toList
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
AddZero.toZero
toList_symm 📖mathematicalEquiv.symm
FreeAddMonoid
toList
ofList
toList_zero 📖mathematicalDFunLike.coe
Equiv
FreeAddMonoid
EquivLike.toFunLike
Equiv.instEquivLike
toList
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
vadd_def 📖mathematicalHVAdd.hVAdd
FreeAddMonoid
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
AddRightCancelMonoid.toAddMonoid
AddCancelMonoid.toAddRightCancelMonoid
instAddCancelMonoid
AddAction.toAddSemigroupAction
mkAddAction
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
toList
zero_ne_of 📖of_ne_zero

FreeMonoid

Definitions

NameCategoryTheorems
casesOn 📖CompOp
freeMonoidCongr 📖CompOp
2 mathmath: freeMonoidCongr_of, freeMonoidCongr_symm_of
instCancelMonoid 📖CompOp
86 mathmath: map_apply_map_symm_eq, freeMonoidCongr_of, toList_prod, ofList_smul, hom_eq_iff, countP'_mul, Monoid.Coprod.con_ker_mk, Monoid.Foldl.ofFreeMonoid_apply, lift_restrict, Traversable.foldMap_hom_free, Traversable.foldlm.ofFreeMonoid_comp_of, countP_of, ofList_append, toList_mul, mem_mul, lift_of_comp_eq_map, lift_ofList, mem_map, Monoid.Coprod.con_inv_mul_cancel, lift_comp_of, of_smul, Monoid.fg_iff_exists_freeMonoid_hom_surjective, length_eq_zero, star_one, map_surjective, closure_range_of, map_map, countP'_one, ofList_nil, count_of, recOn_of_mul, comp_lift, reverse_mul, lift_eval_of, toList_of_mul, Monoid.CoprodI.of_apply, ofList_cons, Traversable.foldl.unop_ofFreeMonoid, toList_map, Monoid.foldlM.ofFreeMonoid_apply, instTwoUniqueProds, Monoid.Coprod.mk_of_inr, mrange_lift, casesOn_one, Traversable.foldr.ofFreeMonoid_comp_of, Traversable.foldrm.ofFreeMonoid_comp_of, hom_map_lift, Monoid.Coprod.mrange_mk, notMem_one, length_mul, lift_symm_apply, Monoid.Coprod.inv_def, map_id, Monoid.Coprod.mk_of_inl, Traversable.Free.map_eq_map, star_of, Traversable.foldl.ofFreeMonoid_comp_of, Monoid.Foldr.ofFreeMonoid_apply, smul_def, lift_apply, symbols_one, ofList_flatten, symbols_mul, Monoid.Coprod.mk_surjective, map_comp, Monoid.Coprod.lift_apply_mk, length_one, countP_apply, freeMonoidCongr_symm_of, Monoid.Coprod.map_mk_ofList, count_apply, map_symm_apply_map_eq, map_of, ofList_map, Monoid.foldrM.ofFreeMonoid_apply, toList_one, PresentedMonoid.surjective_mk, recOn_one, Monoid.Coprod.mk_of_inv_mul, Monoid.Coprod.mk_eq_mk, casesOn_of_mul, Traversable.toList_spec, length_eq_three, Submonoid.closure_eq_mrange, length_eq_two, length_eq_four
instInhabited 📖CompOp
instMembership 📖CompOp
6 mathmath: mem_mul, mem_map, mem_symbols, mem_of_self, mem_of, notMem_one
instUniqueOfIsEmpty 📖CompOp
length 📖CompOp
9 mathmath: length_eq_one, length_eq_zero, length_of, length_reverse, length_mul, length_one, length_eq_three, length_eq_two, length_eq_four
map 📖CompOp
12 mathmath: map_apply_map_symm_eq, lift_of_comp_eq_map, mem_map, map_surjective, map_map, toList_map, map_id, Traversable.Free.map_eq_map, map_comp, map_symm_apply_map_eq, map_of, ofList_map
mem 📖MathDef
mkMulAction 📖CompOp
3 mathmath: ofList_smul, of_smul, smul_def
of 📖CompOp
40 mathmath: freeMonoidCongr_of, hom_eq_iff, lift_restrict, Traversable.foldMap_hom_free, Traversable.foldlm.ofFreeMonoid_comp_of, countP_of, length_eq_one, lift_of_comp_eq_map, lift_comp_of, of_smul, closure_range_of, toList_of, mem_of_self, count_of, recOn_of_mul, of_injective, lift_eval_of, toList_of_mul, Monoid.CoprodI.of_apply, ofList_cons, mem_of, length_of, Monoid.Coprod.mk_of_inr, symbols_of, ofList_singleton, Traversable.foldr.ofFreeMonoid_comp_of, Traversable.foldrm.ofFreeMonoid_comp_of, lift_symm_apply, Monoid.Coprod.mk_of_inl, star_of, Traversable.foldl.ofFreeMonoid_comp_of, reverse_of, freeMonoidCongr_symm_of, map_of, Monoid.Coprod.mk_of_inv_mul, casesOn_of_mul, Traversable.toList_spec, length_eq_three, length_eq_two, length_eq_four
ofList 📖CompOp
18 mathmath: ofList_smul, ofList_append, toList_ofList, lift_ofList, Monoid.Coprod.con_inv_mul_cancel, ofList_toList, ofList_nil, ofList_symm, ofList_cons, toList_symm, ofList_singleton, Monoid.Coprod.inv_def, Traversable.Free.map_eq_map, ofList_flatten, ofList_comp_toList, Monoid.Coprod.map_mk_ofList, ofList_map, toList_comp_ofList
prodAux 📖CompOp
1 mathmath: prodAux_eq
recOn 📖CompOp
reverse 📖CompOp
4 mathmath: reverse_reverse, reverse_mul, length_reverse, reverse_of
toList 📖CompOp
26 mathmath: toList_prod, Monoid.Foldl.ofFreeMonoid_apply, toList_mul, toList_nil, toList_ofList, Monoid.Coprod.con_inv_mul_cancel, ofList_toList, toList_of, toList_cons, toList_of_mul, ofList_symm, Traversable.foldl.unop_ofFreeMonoid, toList_map, Monoid.foldlM.ofFreeMonoid_apply, toList_symm, Monoid.Coprod.inv_def, Traversable.Free.map_eq_map, Monoid.Foldr.ofFreeMonoid_apply, smul_def, lift_apply, ofList_comp_toList, countP_apply, Monoid.foldrM.ofFreeMonoid_apply, toList_one, toList_comp_ofList, Traversable.toList_spec
uniqueUnits 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
casesOn_of_mul 📖mathematicalFreeMonoid
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
of
casesOn_one 📖mathematicalFreeMonoid
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
comp_lift 📖mathematicalMonoidHom.comp
FreeMonoid
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
DFunLike.coe
Equiv
MonoidHom
EquivLike.toFunLike
Equiv.instEquivLike
lift
MonoidHom.instFunLike
hom_eq
freeMonoidCongr_of 📖mathematicalDFunLike.coe
MulEquiv
FreeMonoid
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
EquivLike.toFunLike
MulEquiv.instEquivLike
freeMonoidCongr
of
Equiv
Equiv.instEquivLike
freeMonoidCongr_symm_of 📖mathematicalDFunLike.coe
MulEquiv
FreeMonoid
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
EquivLike.toFunLike
MulEquiv.instEquivLike
freeMonoidCongr
Equiv.symm
of
Equiv
Equiv.instEquivLike
hom_eq 📖DFunLike.coe
MonoidHom
FreeMonoid
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
MonoidHom.instFunLike
of
MonoidHom.ext
MonoidHom.map_one
map_mul
MonoidHomClass.toMulHomClass
MonoidHom.instMonoidHomClass
hom_eq_iff 📖mathematicalDFunLike.coe
MonoidHom
FreeMonoid
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
MonoidHom.instFunLike
of
hom_eq
hom_map_lift 📖mathematicalDFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
MonoidHom.instFunLike
FreeMonoid
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
DFunLike.ext_iff
comp_lift
inductionOn 📖FreeMonoid
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
of
MulOne.toMul
inductionOn' 📖FreeMonoid
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
MulOne.toMul
of
length_eq_four 📖mathematicallength
FreeMonoid
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
of
List.length_eq_four
length_eq_one 📖mathematicallength
of
length_eq_three 📖mathematicallength
FreeMonoid
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
of
List.length_eq_three
length_eq_two 📖mathematicallength
FreeMonoid
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
of
List.length_eq_two
length_eq_zero 📖mathematicallength
FreeMonoid
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
length_mul 📖mathematicallength
FreeMonoid
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
length_of 📖mathematicallength
of
length_one 📖mathematicallength
FreeMonoid
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
length_reverse 📖mathematicallength
reverse
lift_apply 📖mathematicalDFunLike.coe
MonoidHom
FreeMonoid
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
MonoidHom.instFunLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
MulOne.toMul
MulOne.toOne
toList
prodAux_eq
lift_comp_of 📖mathematicalFreeMonoid
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
MonoidHom.instFunLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
lift_eval_of 📖mathematicalDFunLike.coe
MonoidHom
FreeMonoid
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
MonoidHom.instFunLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
lift_ofList 📖mathematicalDFunLike.coe
MonoidHom
FreeMonoid
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
MonoidHom.instFunLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
ofList
MulOne.toMul
MulOne.toOne
prodAux_eq
lift_of_comp_eq_map 📖mathematicalDFunLike.coe
Equiv
MonoidHom
FreeMonoid
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
map
hom_eq
lift_restrict 📖mathematicalDFunLike.coe
Equiv
MonoidHom
FreeMonoid
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
EquivLike.toFunLike
Equiv.instEquivLike
lift
MonoidHom.instFunLike
of
Equiv.apply_symm_apply
lift_symm_apply 📖mathematicalDFunLike.coe
Equiv
MonoidHom
FreeMonoid
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
lift
MonoidHom.instFunLike
of
map_apply_map_symm_eq 📖mathematicalDFunLike.coe
MonoidHom
FreeMonoid
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
MonoidHom.instFunLike
map
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
map_map
Equiv.self_comp_symm
map_id
map_comp 📖mathematicalmap
MonoidHom.comp
FreeMonoid
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
hom_eq
map_id 📖mathematicalmap
MonoidHom.id
FreeMonoid
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
hom_eq
map_map 📖mathematicalDFunLike.coe
MonoidHom
FreeMonoid
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
MonoidHom.instFunLike
map
map_of 📖mathematicalDFunLike.coe
MonoidHom
FreeMonoid
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
MonoidHom.instFunLike
map
of
map_surjective 📖mathematicalFreeMonoid
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
MonoidHom.instFunLike
map
inductionOn'
map_one
MonoidHomClass.toOneHomClass
MonoidHom.instMonoidHomClass
map_mul
MonoidHomClass.toMulHomClass
of_injective
mul_one
length_mul
AddLeftCancelSemigroup.toIsLeftCancelAdd
map_symm_apply_map_eq 📖mathematicalDFunLike.coe
MonoidHom
FreeMonoid
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
MonoidHom.instFunLike
map
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
map_map
Equiv.symm_comp_self
map_id
mem_map 📖mathematicalFreeMonoid
instMembership
DFunLike.coe
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
MonoidHom.instFunLike
map
mem_mul 📖mathematicalFreeMonoid
instMembership
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
mem_of 📖mathematicalFreeMonoid
instMembership
of
mem_of_self 📖mathematicalFreeMonoid
instMembership
of
notMem_one 📖mathematicalFreeMonoid
instMembership
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
ofList_append 📖mathematicalDFunLike.coe
Equiv
FreeMonoid
EquivLike.toFunLike
Equiv.instEquivLike
ofList
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
ofList_comp_toList 📖mathematicalFreeMonoid
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
ofList
toList
ofList_cons 📖mathematicalDFunLike.coe
Equiv
FreeMonoid
EquivLike.toFunLike
Equiv.instEquivLike
ofList
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
of
ofList_flatten 📖mathematicalDFunLike.coe
Equiv
FreeMonoid
EquivLike.toFunLike
Equiv.instEquivLike
ofList
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
MulOne.toOne
Equiv.injective
toList_prod
ofList_map 📖mathematicalDFunLike.coe
Equiv
FreeMonoid
EquivLike.toFunLike
Equiv.instEquivLike
ofList
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
MonoidHom.instFunLike
map
ofList_nil 📖mathematicalDFunLike.coe
Equiv
FreeMonoid
EquivLike.toFunLike
Equiv.instEquivLike
ofList
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
ofList_singleton 📖mathematicalDFunLike.coe
Equiv
FreeMonoid
EquivLike.toFunLike
Equiv.instEquivLike
ofList
of
ofList_smul 📖mathematicalFreeMonoid
SemigroupAction.toSMul
Monoid.toSemigroup
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
MulAction.toSemigroupAction
mkMulAction
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
ofList
ofList_symm 📖mathematicalEquiv.symm
FreeMonoid
ofList
toList
ofList_toList 📖mathematicalDFunLike.coe
Equiv
FreeMonoid
EquivLike.toFunLike
Equiv.instEquivLike
ofList
toList
of_injective 📖mathematicalFreeMonoid
of
List.singleton_injective
of_ne_one 📖
of_smul 📖mathematicalFreeMonoid
SemigroupAction.toSMul
Monoid.toSemigroup
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
MulAction.toSemigroupAction
mkMulAction
of
one_ne_of 📖of_ne_one
prodAux_eq 📖mathematicalprodAux
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
MulOne.toOne
Semigroup.to_isAssociative
Semigroup.to_isLawfulIdentity
one_mul
recOn_of_mul 📖mathematicalFreeMonoid
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
of
recOn_one 📖mathematicalFreeMonoid
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
reverse_mul 📖mathematicalreverse
FreeMonoid
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
reverse_of 📖mathematicalreverse
of
reverse_reverse 📖mathematicalreverse
smul_def 📖mathematicalFreeMonoid
SemigroupAction.toSMul
Monoid.toSemigroup
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
MulAction.toSemigroupAction
mkMulAction
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
toList
toList_comp_ofList 📖mathematicalFreeMonoid
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
toList
ofList
toList_cons 📖mathematicalDFunLike.coe
Equiv
FreeMonoid
EquivLike.toFunLike
Equiv.instEquivLike
toList
toList_map 📖mathematicalDFunLike.coe
Equiv
FreeMonoid
EquivLike.toFunLike
Equiv.instEquivLike
toList
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
MonoidHom.instFunLike
map
toList_mul 📖mathematicalDFunLike.coe
Equiv
FreeMonoid
EquivLike.toFunLike
Equiv.instEquivLike
toList
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
toList_nil 📖mathematicalDFunLike.coe
Equiv
FreeMonoid
EquivLike.toFunLike
Equiv.instEquivLike
toList
toList_of 📖mathematicalDFunLike.coe
Equiv
FreeMonoid
EquivLike.toFunLike
Equiv.instEquivLike
toList
of
toList_ofList 📖mathematicalDFunLike.coe
Equiv
FreeMonoid
EquivLike.toFunLike
Equiv.instEquivLike
toList
ofList
toList_of_mul 📖mathematicalDFunLike.coe
Equiv
FreeMonoid
EquivLike.toFunLike
Equiv.instEquivLike
toList
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
of
toList_one 📖mathematicalDFunLike.coe
Equiv
FreeMonoid
EquivLike.toFunLike
Equiv.instEquivLike
toList
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
toList_prod 📖mathematicalDFunLike.coe
Equiv
FreeMonoid
EquivLike.toFunLike
Equiv.instEquivLike
toList
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
RightCancelMonoid.toMonoid
CancelMonoid.toRightCancelMonoid
instCancelMonoid
MulOne.toOne
toList_symm 📖mathematicalEquiv.symm
FreeMonoid
toList
ofList

(root)

Definitions

NameCategoryTheorems
FreeAddMonoid 📖CompOp
99 mathmath: FreeAddMonoid.lift_symm_apply, FreeAddMonoid.casesOn_zero, FreeAddMonoid.length_zero, FreeAddMonoid.length_eq_zero, FreeAddMonoid.toList_sum, FreeAddMonoid.lift_ofList, FreeAddMonoid.count_apply, AddMonoid.Coprod.mk_of_inr, FreeAddMonoid.toPiTensorProduct, FreeAddMonoid.lift_apply, FreeAddMonoid.toList_comp_ofList, FreeAddMonoid.length_add, PresentedAddMonoid.surjective_mk, FreeAddMonoid.count_of, PiTensorProduct.projectiveSeminormAux_smul, FreeAddMonoid.mem_add, AddMonoid.Coprod.neg_def, FreeAddMonoid.vadd_def, FreeAddMonoid.mem_map, PiTensorProduct.projectiveSeminorm_apply, FreeAddMonoid.map_comp, FreeAddMonoid.recOn_of_add, FreeAddMonoid.mem_of, FreeAddMonoid.mem_of_self, FreeAddMonoid.ofList_append, FreeAddMonoid.ofList_vadd, FreeAddMonoid.ofList_map, FreeAddMonoid.map_surjective, PiTensorProduct.bddBelow_projectiveSemiNormAux, FreeAddMonoid.toList_of, FreeAddMonoid.toList_zero, FreeAddMonoid.ofList_cons, FreeAddMonoid.reverse_add, FreeAddMonoid.toList_add, PiTensorProduct.lifts_zero, FreeAddMonoid.notMem_zero, FreeAddMonoid.ofList_nil, FreeAddMonoid.toList_map, FreeAddMonoid.freeAddMonoidCongr_of, Cardinal.mk_freeAddMonoid, FreeAddMonoid.ofList_symm, AddMonoid.Coprod.mk_surjective, FreeAddMonoid.ofList_toList, AddMonoid.Coprod.mk_of_neg_add, FreeAddMonoid.toList_of_add, FreeAddMonoid.countP'_add, AddMonoid.fg_iff_exists_freeAddMonoid_hom_surjective, FreeAddMonoid.map_id, FreeAddMonoid.lift_comp_of, FreeAddMonoid.freeAddMonoidCongr_symm_of, FreeAddMonoid.closure_range_of, AddMonoid.Coprod.map_mk_ofList, AddMonoid.Coprod.mk_eq_mk, PiTensorProduct.mem_lifts_iff, FreeAddMonoid.casesOn_of_add, TensorProduct.SMul.aux_of, FreeAddMonoid.symbols_zero, FreeAddMonoid.lift_eval_of, FreeAddMonoid.mrange_lift, FreeAddMonoid.recOn_zero, FreeAddMonoid.mem_symbols, FreeAddMonoid.lift_restrict, FreeAddMonoid.length_eq_three, AddMonoid.Coprod.lift_apply_mk, AddMonoid.Coprod.mrange_mk, FreeAddMonoid.instTwoUniqueSums, FreeAddMonoid.length_eq_two, instCountableFreeAddMonoid, FreeAddMonoid.map_symm_apply_map_eq, FreeAddMonoid.countP'_zero, FreeAddMonoid.comp_lift, FreeAddMonoid.ofList_flatten, FreeAddMonoid.lift_of_comp_eq_map, FreeAddMonoid.map_of, FreeAddMonoid.map_apply_map_symm_eq, instInfiniteFreeAddMonoidOfNonempty, FreeAddMonoid.toList_ofList, AddMonoid.Coprod.con_ker_mk, FreeAddMonoid.toList_symm, FreeAddMonoid.countP_apply, FreeAddMonoid.of_vadd, FreeAddMonoid.ofList_comp_toList, FreeAddMonoid.symbols_add, FreeAddMonoid.hom_map_lift, FreeAddMonoid.map_map, FreeMonoid.count_apply, FreeAddMonoid.countP_of, FreeAddMonoid.toList_cons, CharacterModule.homEquiv_apply_apply, AddSubmonoid.closure_eq_mrange, AddMonoid.Coprod.mk_of_inl, FreeAddMonoid.ofList_singleton, FreeAddMonoid.hom_eq_iff, PiTensorProduct.nonempty_lifts, FreeAddMonoid.toList_nil, FreeAddMonoid.of_injective, FreeAddMonoid.length_eq_four, AddMonoid.Coprod.con_neg_add_cancel, PiTensorProduct.projectiveSeminormAux_add_le
FreeMonoid 📖CompOp
104 mathmath: FreeMonoid.map_apply_map_symm_eq, FreeMonoid.freeMonoidCongr_of, FreeMonoid.toList_prod, FreeMonoid.ofList_smul, FreeMonoid.hom_eq_iff, FreeMonoid.countP'_mul, Monoid.Coprod.con_ker_mk, Monoid.Foldl.ofFreeMonoid_apply, FreeMonoid.lift_restrict, Traversable.foldMap_hom_free, Traversable.foldlm.ofFreeMonoid_comp_of, FreeMonoid.countP_of, FreeMonoid.ofList_append, FreeMonoid.toList_mul, FreeMonoid.toList_nil, FreeMonoid.mem_mul, FreeMonoid.toList_ofList, FreeMonoid.lift_of_comp_eq_map, FreeMonoid.lift_ofList, FreeMonoid.mem_map, Monoid.Coprod.con_inv_mul_cancel, FreeMonoid.lift_comp_of, FreeMonoid.of_smul, Monoid.fg_iff_exists_freeMonoid_hom_surjective, FreeMonoid.length_eq_zero, Cardinal.mk_freeMonoid, FreeMonoid.mem_symbols, FreeMonoid.star_one, FreeMonoid.map_surjective, FreeMonoid.ofList_toList, FreeMonoid.closure_range_of, FreeMonoid.toList_of, FreeMonoid.mem_of_self, FreeMonoid.map_map, FreeMonoid.countP'_one, FreeMonoid.ofList_nil, FreeMonoid.count_of, FreeMonoid.toList_cons, FreeMonoid.recOn_of_mul, FreeMonoid.of_injective, FreeMonoid.comp_lift, FreeMonoid.reverse_mul, FreeMonoid.lift_eval_of, FreeMonoid.toList_of_mul, FreeMonoid.ofList_symm, Monoid.CoprodI.of_apply, FreeMonoid.ofList_cons, Traversable.foldl.unop_ofFreeMonoid, FreeMonoid.toList_map, Monoid.foldlM.ofFreeMonoid_apply, FreeMonoid.mem_of, FreeMonoid.toList_symm, FreeMonoid.instTwoUniqueProds, Monoid.Coprod.mk_of_inr, FreeMonoid.mrange_lift, FreeMonoid.casesOn_one, FreeMonoid.ofList_singleton, Traversable.foldr.ofFreeMonoid_comp_of, Traversable.foldrm.ofFreeMonoid_comp_of, Module.Basis.tensorAlgebra_repr_apply, FreeMonoid.hom_map_lift, Monoid.Coprod.mrange_mk, FreeMonoid.notMem_one, FreeMonoid.length_mul, FreeMonoid.lift_symm_apply, Monoid.Coprod.inv_def, FreeMonoid.map_id, Monoid.Coprod.mk_of_inl, Traversable.Free.map_eq_map, FreeMonoid.star_of, Traversable.foldl.ofFreeMonoid_comp_of, Monoid.Foldr.ofFreeMonoid_apply, FreeMonoid.smul_def, FreeMonoid.lift_apply, FreeMonoid.symbols_one, FreeMonoid.ofList_flatten, FreeMonoid.symbols_mul, Monoid.Coprod.mk_surjective, FreeMonoid.map_comp, Monoid.Coprod.lift_apply_mk, FreeMonoid.length_one, instInfiniteFreeMonoidOfNonempty, FreeMonoid.ofList_comp_toList, FreeMonoid.countP_apply, FreeMonoid.freeMonoidCongr_symm_of, Monoid.Coprod.map_mk_ofList, FreeMonoid.count_apply, FreeMonoid.map_symm_apply_map_eq, FreeMonoid.map_of, FreeMonoid.ofList_map, Monoid.foldrM.ofFreeMonoid_apply, FreeMonoid.toList_one, instCountableFreeMonoid, PresentedMonoid.surjective_mk, FreeMonoid.recOn_one, FreeMonoid.toList_comp_ofList, Monoid.Coprod.mk_of_inv_mul, Monoid.Coprod.mk_eq_mk, FreeMonoid.casesOn_of_mul, Traversable.toList_spec, FreeMonoid.length_eq_three, Submonoid.closure_eq_mrange, FreeMonoid.length_eq_two, FreeMonoid.length_eq_four

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