Documentation Verification Report

Free

📁 Source: Mathlib/Algebra/Free.lean

Statistics

MetricCount
DefinitionsAssocRel, FreeAddSemigroup, instAddSemigroup, instInhabited, map, of, FreeAddMagma, instAdd, instInhabited, instMonad, instTraversable, length, liftAux, map, recOnAdd, recOnPure, repr, toFreeAddSemigroup, traverse, FreeAddMagmaAssocQuotientEquiv, FreeAddSemigroup, head, instAddSemigroup, instDecidableEq, instInhabited, instMonad, instTraversable, length, map, of, recOnAdd, recOnPure, tail, traverse, FreeMagma, instInhabited, instMonad, instMul, instTraversable, length, liftAux, map, recOnMul, recOnPure, repr, toFreeSemigroup, traverse, FreeMagmaAssocQuotientEquiv, FreeSemigroup, head, instDecidableEq, instInhabited, instMonad, instSemigroup, instTraversable, length, map, of, recOnMul, recOnPure, tail, traverse, AssocQuotient, instInhabited, instSemigroup, map, of, AssocRel, instDecidableEqFreeAddMagma, decEq, instDecidableEqFreeMagma, decEq, instReprFreeAddMagma, instReprFreeMagma
74
Theoremshom_ext, hom_ext_iff, induction_on, lift_comp_of, lift_comp_of', lift_of, lift_symm_apply, map_of, quot_mk_assoc, quot_mk_assoc_left, add_bind, add_eq, add_seq, hom_ext, hom_ext_iff, instLawfulMonad, instLawfulTraversable, length_pos, length_toFreeAddSemigroup, lift_comp_of, lift_comp_of', lift_of, lift_symm_apply, map_add', map_of, map_pure, pure_bind, pure_seq, toFreeAddSemigroup_comp_map, toFreeAddSemigroup_comp_of, toFreeAddSemigroup_map, toFreeAddSemigroup_of, traverse_add, traverse_add', traverse_eq, traverse_pure, traverse_pure', add_bind, add_seq, ext, ext_iff, head_add, hom_ext, hom_ext_iff, instLawfulMonad, instLawfulTraversable, length_add, length_map, length_of, lift_comp_of, lift_comp_of', lift_of, lift_of_add, lift_symm_apply, map_add', map_of, map_pure, mk_add_mk, of_head, of_tail, pure_bind, pure_seq, tail_add, traverse_add, traverse_add', traverse_eq, traverse_pure, traverse_pure', hom_ext, hom_ext_iff, instLawfulMonad, instLawfulTraversable, length_pos, length_toFreeSemigroup, lift_comp_of, lift_comp_of', lift_of, lift_symm_apply, map_mul', map_of, map_pure, mul_bind, mul_eq, mul_seq, pure_bind, pure_seq, toFreeSemigroup_comp_map, toFreeSemigroup_comp_of, toFreeSemigroup_map, toFreeSemigroup_of, traverse_eq, traverse_mul, traverse_mul', traverse_pure, traverse_pure', ext, ext_iff, head_mul, hom_ext, hom_ext_iff, instLawfulMonad, instLawfulTraversable, length_map, length_mul, length_of, lift_comp_of, lift_comp_of', lift_of, lift_of_mul, lift_symm_apply, map_mul', map_of, map_pure, mk_mul_mk, mul_bind, mul_seq, of_head, of_tail, pure_bind, pure_seq, tail_mul, traverse_eq, traverse_mul, traverse_mul', traverse_pure, traverse_pure', hom_ext, hom_ext_iff, induction_on, lift_comp_of, lift_comp_of', lift_of, lift_symm_apply, map_of, quot_mk_assoc, quot_mk_assoc_left
136
Total210

AddMagma

Definitions

NameCategoryTheorems
AssocRel 📖CompData
2 mathmath: FreeAddSemigroup.quot_mk_assoc, FreeAddSemigroup.quot_mk_assoc_left
FreeAddSemigroup 📖CompOp
6 mathmath: FreeAddSemigroup.lift_symm_apply, FreeAddSemigroup.lift_comp_of, FreeAddSemigroup.lift_comp_of', FreeAddSemigroup.lift_of, FreeAddSemigroup.hom_ext_iff, FreeAddSemigroup.map_of

AddMagma.FreeAddSemigroup

Definitions

NameCategoryTheorems
instAddSemigroup 📖CompOp
6 mathmath: lift_symm_apply, lift_comp_of, lift_comp_of', lift_of, hom_ext_iff, map_of
instInhabited 📖CompOp
map 📖CompOp
1 mathmath: map_of
of 📖CompOp
6 mathmath: lift_symm_apply, lift_comp_of, lift_comp_of', lift_of, hom_ext_iff, map_of

Theorems

NameKindAssumesProvesValidatesDepends On
hom_ext 📖AddHom.comp
AddMagma.FreeAddSemigroup
AddSemigroup.toAdd
instAddSemigroup
of
DFunLike.ext
induction_on
DFunLike.congr_fun
hom_ext_iff 📖mathematicalAddHom.comp
AddMagma.FreeAddSemigroup
AddSemigroup.toAdd
instAddSemigroup
of
hom_ext
induction_on 📖DFunLike.coe
AddHom
AddMagma.FreeAddSemigroup
AddSemigroup.toAdd
instAddSemigroup
AddHom.funLike
of
Quot.induction_on
lift_comp_of 📖mathematicalAddHom.comp
AddMagma.FreeAddSemigroup
AddSemigroup.toAdd
instAddSemigroup
DFunLike.coe
Equiv
AddHom
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
Equiv.symm_apply_apply
lift_comp_of' 📖mathematicalDFunLike.coe
Equiv
AddHom
AddSemigroup.toAdd
AddMagma.FreeAddSemigroup
instAddSemigroup
EquivLike.toFunLike
Equiv.instEquivLike
lift
AddHom.comp
of
Equiv.apply_symm_apply
lift_of 📖mathematicalDFunLike.coe
AddHom
AddMagma.FreeAddSemigroup
AddSemigroup.toAdd
instAddSemigroup
AddHom.funLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
lift_symm_apply 📖mathematicalDFunLike.coe
Equiv
AddHom
AddMagma.FreeAddSemigroup
AddSemigroup.toAdd
instAddSemigroup
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
lift
AddHom.comp
of
map_of 📖mathematicalDFunLike.coe
AddHom
AddMagma.FreeAddSemigroup
AddSemigroup.toAdd
instAddSemigroup
AddHom.funLike
map
of
quot_mk_assoc 📖mathematicalAddMagma.AssocRel
quot_mk_assoc_left 📖mathematicalAddMagma.AssocRel

FreeAddMagma

Definitions

NameCategoryTheorems
instAdd 📖CompOp
17 mathmath: traverse_add, toFreeAddSemigroup_comp_of, add_bind, lift_comp_of, toFreeAddSemigroup_comp_map, add_eq, map_of, lift_comp_of', traverse_add', toFreeAddSemigroup_of, toFreeAddSemigroup_map, lift_symm_apply, map_add', hom_ext_iff, add_seq, lift_of, length_toFreeAddSemigroup
instInhabited 📖CompOp
instMonad 📖CompOp
9 mathmath: add_bind, map_pure, instLawfulMonad, traverse_pure', pure_seq, map_add', add_seq, pure_bind, traverse_pure
instTraversable 📖CompOp
6 mathmath: traverse_add, traverse_eq, traverse_pure', traverse_add', instLawfulTraversable, traverse_pure
length 📖CompOp
2 mathmath: length_pos, length_toFreeAddSemigroup
liftAux 📖CompOp
map 📖CompOp
3 mathmath: toFreeAddSemigroup_comp_map, map_of, toFreeAddSemigroup_map
recOnAdd 📖CompOp
recOnPure 📖CompOp
repr 📖CompOp
toFreeAddSemigroup 📖CompOp
5 mathmath: toFreeAddSemigroup_comp_of, toFreeAddSemigroup_comp_map, toFreeAddSemigroup_of, toFreeAddSemigroup_map, length_toFreeAddSemigroup
traverse 📖CompOp
1 mathmath: traverse_eq

Theorems

NameKindAssumesProvesValidatesDepends On
add_bind 📖mathematicalFreeAddMagma
instMonad
instAdd
add_eq 📖mathematicaladd
FreeAddMagma
instAdd
add_seq 📖mathematicalFreeAddMagma
instMonad
instAdd
hom_ext 📖FreeAddMagma
DFunLike.coe
AddHom
instAdd
AddHom.funLike
of
DFunLike.ext
map_add
AddHom.addHomClass
hom_ext_iff 📖mathematicalFreeAddMagma
DFunLike.coe
AddHom
instAdd
AddHom.funLike
of
hom_ext
instLawfulMonad 📖mathematicalFreeAddMagma
instMonad
map_add'
add_bind
instLawfulTraversable 📖mathematicalLawfulTraversable
FreeAddMagma
instTraversable
instLawfulMonad
traverse_add
CommApplicative.toLawfulApplicative
instCommApplicativeId
seq_map_assoc
map_seq
map_add'
ApplicativeTransformation.preserves_map
ApplicativeTransformation.preserves_seq
length_pos 📖mathematicallength
length_toFreeAddSemigroup 📖mathematicalFreeAddSemigroup.length
DFunLike.coe
AddHom
FreeAddMagma
FreeAddSemigroup
instAdd
AddSemigroup.toAdd
FreeAddSemigroup.instAddSemigroup
AddHom.funLike
toFreeAddSemigroup
length
map_add
AddHom.addHomClass
FreeAddSemigroup.length_add
lift_comp_of 📖mathematicalFreeAddMagma
DFunLike.coe
AddHom
instAdd
AddHom.funLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
lift_comp_of' 📖mathematicalDFunLike.coe
Equiv
AddHom
FreeAddMagma
instAdd
EquivLike.toFunLike
Equiv.instEquivLike
lift
AddHom.funLike
of
Equiv.apply_symm_apply
lift_of 📖mathematicalDFunLike.coe
AddHom
FreeAddMagma
instAdd
AddHom.funLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
lift_symm_apply 📖mathematicalDFunLike.coe
Equiv
AddHom
FreeAddMagma
instAdd
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
lift
AddHom.funLike
of
map_add' 📖mathematicalFreeAddMagma
instMonad
instAdd
map_of 📖mathematicalDFunLike.coe
AddHom
FreeAddMagma
instAdd
AddHom.funLike
map
of
map_pure 📖mathematicalFreeAddMagma
instMonad
pure_bind 📖mathematicalFreeAddMagma
instMonad
pure_seq 📖mathematicalFreeAddMagma
instMonad
toFreeAddSemigroup_comp_map 📖mathematicalAddHom.comp
FreeAddMagma
FreeAddSemigroup
instAdd
AddSemigroup.toAdd
FreeAddSemigroup.instAddSemigroup
toFreeAddSemigroup
map
FreeAddSemigroup.map
hom_ext
toFreeAddSemigroup_comp_of 📖mathematicalFreeAddMagma
FreeAddSemigroup
DFunLike.coe
AddHom
instAdd
AddSemigroup.toAdd
FreeAddSemigroup.instAddSemigroup
AddHom.funLike
toFreeAddSemigroup
of
FreeAddSemigroup.of
toFreeAddSemigroup_map 📖mathematicalDFunLike.coe
AddHom
FreeAddMagma
FreeAddSemigroup
instAdd
AddSemigroup.toAdd
FreeAddSemigroup.instAddSemigroup
AddHom.funLike
toFreeAddSemigroup
map
FreeAddSemigroup.map
DFunLike.congr_fun
toFreeAddSemigroup_comp_map
toFreeAddSemigroup_of 📖mathematicalDFunLike.coe
AddHom
FreeAddMagma
FreeAddSemigroup
instAdd
AddSemigroup.toAdd
FreeAddSemigroup.instAddSemigroup
AddHom.funLike
toFreeAddSemigroup
of
FreeAddSemigroup.of
traverse_add 📖mathematicalTraversable.traverse
FreeAddMagma
instTraversable
instAdd
traverse_add' 📖mathematicalFreeAddMagma
Traversable.traverse
instTraversable
instAdd
traverse_eq 📖mathematicaltraverse
Traversable.traverse
FreeAddMagma
instTraversable
traverse_pure 📖mathematicalTraversable.traverse
FreeAddMagma
instTraversable
instMonad
traverse_pure' 📖mathematicalFreeAddMagma
Traversable.traverse
instTraversable
instMonad

FreeAddSemigroup

Definitions

NameCategoryTheorems
head 📖CompOp
4 mathmath: ext_iff, of_head, tail_add, head_add
instAddSemigroup 📖CompOp
22 mathmath: lift_comp_of, add_seq, lift_symm_apply, mk_add_mk, FreeAddMagma.toFreeAddSemigroup_comp_of, lift_of, FreeAddMagma.toFreeAddSemigroup_comp_map, length_add, map_add', traverse_add, length_map, traverse_add', map_of, FreeAddMagma.toFreeAddSemigroup_of, FreeAddMagma.toFreeAddSemigroup_map, tail_add, add_bind, hom_ext_iff, FreeAddMagma.length_toFreeAddSemigroup, lift_of_add, lift_comp_of', head_add
instDecidableEq 📖CompOp
instInhabited 📖CompOp
instMonad 📖CompOp
9 mathmath: map_pure, add_seq, pure_seq, instLawfulMonad, traverse_pure', map_add', traverse_pure, pure_bind, add_bind
instTraversable 📖CompOp
6 mathmath: traverse_pure', traverse_add, traverse_add', traverse_pure, traverse_eq, instLawfulTraversable
length 📖CompOp
4 mathmath: length_add, length_of, length_map, FreeAddMagma.length_toFreeAddSemigroup
map 📖CompOp
4 mathmath: FreeAddMagma.toFreeAddSemigroup_comp_map, length_map, map_of, FreeAddMagma.toFreeAddSemigroup_map
of 📖CompOp
12 mathmath: lift_comp_of, lift_symm_apply, FreeAddMagma.toFreeAddSemigroup_comp_of, lift_of, length_of, map_of, FreeAddMagma.toFreeAddSemigroup_of, of_head, hom_ext_iff, lift_of_add, lift_comp_of', of_tail
recOnAdd 📖CompOp
recOnPure 📖CompOp
tail 📖CompOp
3 mathmath: ext_iff, tail_add, of_tail
traverse 📖CompOp
1 mathmath: traverse_eq

Theorems

NameKindAssumesProvesValidatesDepends On
add_bind 📖mathematicalFreeAddSemigroup
instMonad
AddSemigroup.toAdd
instAddSemigroup
map_add
AddHom.addHomClass
add_seq 📖mathematicalFreeAddSemigroup
instMonad
AddSemigroup.toAdd
instAddSemigroup
add_bind
ext 📖head
tail
ext_iff 📖mathematicalhead
tail
ext
head_add 📖mathematicalhead
FreeAddSemigroup
AddSemigroup.toAdd
instAddSemigroup
hom_ext 📖FreeAddSemigroup
DFunLike.coe
AddHom
AddSemigroup.toAdd
instAddSemigroup
AddHom.funLike
of
DFunLike.ext
map_add
AddHom.addHomClass
hom_ext_iff 📖mathematicalFreeAddSemigroup
DFunLike.coe
AddHom
AddSemigroup.toAdd
instAddSemigroup
AddHom.funLike
of
hom_ext
instLawfulMonad 📖mathematicalFreeAddSemigroup
instMonad
map_add'
add_bind
instLawfulTraversable 📖mathematicalLawfulTraversable
FreeAddSemigroup
instTraversable
instLawfulMonad
traverse_add
CommApplicative.toLawfulApplicative
instCommApplicativeId
Functor.Comp.instLawfulApplicativeComp
seq_map_assoc
map_seq
map_add'
ApplicativeTransformation.preserves_map
ApplicativeTransformation.preserves_seq
length_add 📖mathematicallength
FreeAddSemigroup
AddSemigroup.toAdd
instAddSemigroup
length_map 📖mathematicallength
DFunLike.coe
AddHom
FreeAddSemigroup
AddSemigroup.toAdd
instAddSemigroup
AddHom.funLike
map
map_add
AddHom.addHomClass
length_add
length_of 📖mathematicallength
of
lift_comp_of 📖mathematicalFreeAddSemigroup
DFunLike.coe
AddHom
AddSemigroup.toAdd
instAddSemigroup
AddHom.funLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
lift_comp_of' 📖mathematicalDFunLike.coe
Equiv
AddHom
FreeAddSemigroup
AddSemigroup.toAdd
instAddSemigroup
EquivLike.toFunLike
Equiv.instEquivLike
lift
AddHom.funLike
of
hom_ext
lift_of 📖mathematicalDFunLike.coe
AddHom
FreeAddSemigroup
AddSemigroup.toAdd
instAddSemigroup
AddHom.funLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
lift_of_add 📖mathematicalDFunLike.coe
AddHom
FreeAddSemigroup
AddSemigroup.toAdd
instAddSemigroup
AddHom.funLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
map_add
AddHom.addHomClass
lift_of
lift_symm_apply 📖mathematicalDFunLike.coe
Equiv
AddHom
FreeAddSemigroup
AddSemigroup.toAdd
instAddSemigroup
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
lift
AddHom.funLike
of
map_add' 📖mathematicalFreeAddSemigroup
instMonad
AddSemigroup.toAdd
instAddSemigroup
map_add
AddHom.addHomClass
map_of 📖mathematicalDFunLike.coe
AddHom
FreeAddSemigroup
AddSemigroup.toAdd
instAddSemigroup
AddHom.funLike
map
of
map_pure 📖mathematicalFreeAddSemigroup
instMonad
mk_add_mk 📖mathematicalFreeAddSemigroup
AddSemigroup.toAdd
instAddSemigroup
of_head 📖mathematicalhead
of
of_tail 📖mathematicaltail
of
pure_bind 📖mathematicalFreeAddSemigroup
instMonad
pure_seq 📖mathematicalFreeAddSemigroup
instMonad
tail_add 📖mathematicaltail
FreeAddSemigroup
AddSemigroup.toAdd
instAddSemigroup
head
traverse_add 📖mathematicalTraversable.traverse
FreeAddSemigroup
instTraversable
AddSemigroup.toAdd
instAddSemigroup
seq_map_assoc
add_assoc
map_seq
traverse_add' 📖mathematicalFreeAddSemigroup
Traversable.traverse
instTraversable
AddSemigroup.toAdd
instAddSemigroup
traverse_add
traverse_eq 📖mathematicaltraverse
Traversable.traverse
FreeAddSemigroup
instTraversable
traverse_pure 📖mathematicalTraversable.traverse
FreeAddSemigroup
instTraversable
instMonad
traverse_pure' 📖mathematicalFreeAddSemigroup
Traversable.traverse
instTraversable
instMonad

FreeMagma

Definitions

NameCategoryTheorems
instInhabited 📖CompOp
instMonad 📖CompOp
9 mathmath: map_mul', pure_seq, instLawfulMonad, map_pure, pure_bind, traverse_pure, mul_bind, mul_seq, traverse_pure'
instMul 📖CompOp
28 mathmath: lift_of, toFreeSemigroup_of, traverse_mul, FreeNonUnitalNonAssocAlgebra.of_comp_lift, hom_ext_iff, FreeLieAlgebra.Rel.addLeft, FreeNonUnitalNonAssocAlgebra.lift_unique, map_mul', FreeLieAlgebra.liftAux_map_smul, FreeLieAlgebra.liftAux_map_add, FreeNonUnitalNonAssocAlgebra.lift_symm_apply, FreeLieAlgebra.liftAux_map_mul, FreeLieAlgebra.liftAux_spec, lift_symm_apply, toFreeSemigroup_map, toFreeSemigroup_comp_of, lift_comp_of, length_toFreeSemigroup, map_of, mul_bind, traverse_mul', mul_eq, lift_comp_of', toFreeSemigroup_comp_map, FreeNonUnitalNonAssocAlgebra.lift_of_apply, mul_seq, FreeNonUnitalNonAssocAlgebra.hom_ext_iff, FreeNonUnitalNonAssocAlgebra.lift_comp_of
instTraversable 📖CompOp
6 mathmath: traverse_mul, instLawfulTraversable, traverse_pure, traverse_mul', traverse_eq, traverse_pure'
length 📖CompOp
2 mathmath: length_pos, length_toFreeSemigroup
liftAux 📖CompOp
map 📖CompOp
3 mathmath: toFreeSemigroup_map, map_of, toFreeSemigroup_comp_map
recOnMul 📖CompOp
recOnPure 📖CompOp
repr 📖CompOp
toFreeSemigroup 📖CompOp
5 mathmath: toFreeSemigroup_of, toFreeSemigroup_map, toFreeSemigroup_comp_of, length_toFreeSemigroup, toFreeSemigroup_comp_map
traverse 📖CompOp
1 mathmath: traverse_eq

Theorems

NameKindAssumesProvesValidatesDepends On
hom_ext 📖FreeMagma
DFunLike.coe
MulHom
instMul
MulHom.funLike
of
DFunLike.ext
map_mul
MulHom.mulHomClass
hom_ext_iff 📖mathematicalFreeMagma
DFunLike.coe
MulHom
instMul
MulHom.funLike
of
hom_ext
instLawfulMonad 📖mathematicalFreeMagma
instMonad
map_mul'
mul_bind
instLawfulTraversable 📖mathematicalLawfulTraversable
FreeMagma
instTraversable
instLawfulMonad
traverse_mul
CommApplicative.toLawfulApplicative
instCommApplicativeId
seq_map_assoc
map_seq
map_mul'
ApplicativeTransformation.preserves_map
ApplicativeTransformation.preserves_seq
length_pos 📖mathematicallength
length_toFreeSemigroup 📖mathematicalFreeSemigroup.length
DFunLike.coe
MulHom
FreeMagma
FreeSemigroup
instMul
Semigroup.toMul
FreeSemigroup.instSemigroup
MulHom.funLike
toFreeSemigroup
length
map_mul
MulHom.mulHomClass
FreeSemigroup.length_mul
lift_comp_of 📖mathematicalFreeMagma
DFunLike.coe
MulHom
instMul
MulHom.funLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
lift_comp_of' 📖mathematicalDFunLike.coe
Equiv
MulHom
FreeMagma
instMul
EquivLike.toFunLike
Equiv.instEquivLike
lift
MulHom.funLike
of
Equiv.apply_symm_apply
lift_of 📖mathematicalDFunLike.coe
MulHom
FreeMagma
instMul
MulHom.funLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
lift_symm_apply 📖mathematicalDFunLike.coe
Equiv
MulHom
FreeMagma
instMul
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
lift
MulHom.funLike
of
map_mul' 📖mathematicalFreeMagma
instMonad
instMul
map_of 📖mathematicalDFunLike.coe
MulHom
FreeMagma
instMul
MulHom.funLike
map
of
map_pure 📖mathematicalFreeMagma
instMonad
mul_bind 📖mathematicalFreeMagma
instMonad
instMul
mul_eq 📖mathematicalmul
FreeMagma
instMul
mul_seq 📖mathematicalFreeMagma
instMonad
instMul
pure_bind 📖mathematicalFreeMagma
instMonad
pure_seq 📖mathematicalFreeMagma
instMonad
toFreeSemigroup_comp_map 📖mathematicalMulHom.comp
FreeMagma
FreeSemigroup
instMul
Semigroup.toMul
FreeSemigroup.instSemigroup
toFreeSemigroup
map
FreeSemigroup.map
hom_ext
toFreeSemigroup_comp_of 📖mathematicalFreeMagma
FreeSemigroup
DFunLike.coe
MulHom
instMul
Semigroup.toMul
FreeSemigroup.instSemigroup
MulHom.funLike
toFreeSemigroup
of
FreeSemigroup.of
toFreeSemigroup_map 📖mathematicalDFunLike.coe
MulHom
FreeMagma
FreeSemigroup
instMul
Semigroup.toMul
FreeSemigroup.instSemigroup
MulHom.funLike
toFreeSemigroup
map
FreeSemigroup.map
DFunLike.congr_fun
toFreeSemigroup_comp_map
toFreeSemigroup_of 📖mathematicalDFunLike.coe
MulHom
FreeMagma
FreeSemigroup
instMul
Semigroup.toMul
FreeSemigroup.instSemigroup
MulHom.funLike
toFreeSemigroup
of
FreeSemigroup.of
traverse_eq 📖mathematicaltraverse
Traversable.traverse
FreeMagma
instTraversable
traverse_mul 📖mathematicalTraversable.traverse
FreeMagma
instTraversable
instMul
traverse_mul' 📖mathematicalFreeMagma
Traversable.traverse
instTraversable
instMul
traverse_pure 📖mathematicalTraversable.traverse
FreeMagma
instTraversable
instMonad
traverse_pure' 📖mathematicalFreeMagma
Traversable.traverse
instTraversable
instMonad

FreeSemigroup

Definitions

NameCategoryTheorems
head 📖CompOp
4 mathmath: head_mul, tail_mul, of_head, ext_iff
instDecidableEq 📖CompOp
instInhabited 📖CompOp
instMonad 📖CompOp
9 mathmath: traverse_pure', mul_bind, map_pure, mul_seq, traverse_pure, instLawfulMonad, map_mul', pure_bind, pure_seq
instSemigroup 📖CompOp
22 mathmath: FreeMagma.toFreeSemigroup_of, mul_bind, head_mul, tail_mul, traverse_mul', mul_seq, traverse_mul, lift_symm_apply, mk_mul_mk, length_mul, map_mul', FreeMagma.toFreeSemigroup_map, lift_comp_of', FreeMagma.toFreeSemigroup_comp_of, FreeMagma.length_toFreeSemigroup, FreeMagma.toFreeSemigroup_comp_map, length_map, lift_of_mul, hom_ext_iff, lift_comp_of, map_of, lift_of
instTraversable 📖CompOp
6 mathmath: traverse_pure', instLawfulTraversable, traverse_mul', traverse_mul, traverse_pure, traverse_eq
length 📖CompOp
4 mathmath: length_mul, length_of, FreeMagma.length_toFreeSemigroup, length_map
map 📖CompOp
4 mathmath: FreeMagma.toFreeSemigroup_map, FreeMagma.toFreeSemigroup_comp_map, length_map, map_of
of 📖CompOp
12 mathmath: FreeMagma.toFreeSemigroup_of, of_tail, lift_symm_apply, of_head, length_of, lift_comp_of', FreeMagma.toFreeSemigroup_comp_of, lift_of_mul, hom_ext_iff, lift_comp_of, map_of, lift_of
recOnMul 📖CompOp
recOnPure 📖CompOp
tail 📖CompOp
3 mathmath: tail_mul, of_tail, ext_iff
traverse 📖CompOp
1 mathmath: traverse_eq

Theorems

NameKindAssumesProvesValidatesDepends On
ext 📖head
tail
ext_iff 📖mathematicalhead
tail
ext
head_mul 📖mathematicalhead
FreeSemigroup
Semigroup.toMul
instSemigroup
hom_ext 📖FreeSemigroup
DFunLike.coe
MulHom
Semigroup.toMul
instSemigroup
MulHom.funLike
of
DFunLike.ext
map_mul
MulHom.mulHomClass
hom_ext_iff 📖mathematicalFreeSemigroup
DFunLike.coe
MulHom
Semigroup.toMul
instSemigroup
MulHom.funLike
of
hom_ext
instLawfulMonad 📖mathematicalFreeSemigroup
instMonad
map_mul'
mul_bind
instLawfulTraversable 📖mathematicalLawfulTraversable
FreeSemigroup
instTraversable
instLawfulMonad
traverse_mul
CommApplicative.toLawfulApplicative
instCommApplicativeId
Functor.Comp.instLawfulApplicativeComp
seq_map_assoc
map_seq
map_mul'
ApplicativeTransformation.preserves_map
ApplicativeTransformation.preserves_seq
length_map 📖mathematicallength
DFunLike.coe
MulHom
FreeSemigroup
Semigroup.toMul
instSemigroup
MulHom.funLike
map
map_mul
MulHom.mulHomClass
length_mul
length_mul 📖mathematicallength
FreeSemigroup
Semigroup.toMul
instSemigroup
length_of 📖mathematicallength
of
lift_comp_of 📖mathematicalFreeSemigroup
DFunLike.coe
MulHom
Semigroup.toMul
instSemigroup
MulHom.funLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
lift_comp_of' 📖mathematicalDFunLike.coe
Equiv
MulHom
FreeSemigroup
Semigroup.toMul
instSemigroup
EquivLike.toFunLike
Equiv.instEquivLike
lift
MulHom.funLike
of
hom_ext
lift_of 📖mathematicalDFunLike.coe
MulHom
FreeSemigroup
Semigroup.toMul
instSemigroup
MulHom.funLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
lift_of_mul 📖mathematicalDFunLike.coe
MulHom
FreeSemigroup
Semigroup.toMul
instSemigroup
MulHom.funLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
map_mul
MulHom.mulHomClass
lift_of
lift_symm_apply 📖mathematicalDFunLike.coe
Equiv
MulHom
FreeSemigroup
Semigroup.toMul
instSemigroup
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
lift
MulHom.funLike
of
map_mul' 📖mathematicalFreeSemigroup
instMonad
Semigroup.toMul
instSemigroup
map_mul
MulHom.mulHomClass
map_of 📖mathematicalDFunLike.coe
MulHom
FreeSemigroup
Semigroup.toMul
instSemigroup
MulHom.funLike
map
of
map_pure 📖mathematicalFreeSemigroup
instMonad
mk_mul_mk 📖mathematicalFreeSemigroup
Semigroup.toMul
instSemigroup
mul_bind 📖mathematicalFreeSemigroup
instMonad
Semigroup.toMul
instSemigroup
map_mul
MulHom.mulHomClass
mul_seq 📖mathematicalFreeSemigroup
instMonad
Semigroup.toMul
instSemigroup
mul_bind
of_head 📖mathematicalhead
of
of_tail 📖mathematicaltail
of
pure_bind 📖mathematicalFreeSemigroup
instMonad
pure_seq 📖mathematicalFreeSemigroup
instMonad
tail_mul 📖mathematicaltail
FreeSemigroup
Semigroup.toMul
instSemigroup
head
traverse_eq 📖mathematicaltraverse
Traversable.traverse
FreeSemigroup
instTraversable
traverse_mul 📖mathematicalTraversable.traverse
FreeSemigroup
instTraversable
Semigroup.toMul
instSemigroup
seq_map_assoc
mul_assoc
map_seq
traverse_mul' 📖mathematicalFreeSemigroup
Traversable.traverse
instTraversable
Semigroup.toMul
instSemigroup
traverse_mul
traverse_pure 📖mathematicalTraversable.traverse
FreeSemigroup
instTraversable
instMonad
traverse_pure' 📖mathematicalFreeSemigroup
Traversable.traverse
instTraversable
instMonad

Magma

Definitions

NameCategoryTheorems
AssocQuotient 📖CompOp
6 mathmath: AssocQuotient.lift_comp_of', AssocQuotient.lift_comp_of, AssocQuotient.lift_of, AssocQuotient.hom_ext_iff, AssocQuotient.map_of, AssocQuotient.lift_symm_apply
AssocRel 📖CompData
2 mathmath: AssocQuotient.quot_mk_assoc, AssocQuotient.quot_mk_assoc_left

Magma.AssocQuotient

Definitions

NameCategoryTheorems
instInhabited 📖CompOp
instSemigroup 📖CompOp
6 mathmath: lift_comp_of', lift_comp_of, lift_of, hom_ext_iff, map_of, lift_symm_apply
map 📖CompOp
1 mathmath: map_of
of 📖CompOp
6 mathmath: lift_comp_of', lift_comp_of, lift_of, hom_ext_iff, map_of, lift_symm_apply

Theorems

NameKindAssumesProvesValidatesDepends On
hom_ext 📖MulHom.comp
Magma.AssocQuotient
Semigroup.toMul
instSemigroup
of
DFunLike.ext
induction_on
DFunLike.congr_fun
hom_ext_iff 📖mathematicalMulHom.comp
Magma.AssocQuotient
Semigroup.toMul
instSemigroup
of
hom_ext
induction_on 📖DFunLike.coe
MulHom
Magma.AssocQuotient
Semigroup.toMul
instSemigroup
MulHom.funLike
of
Quot.induction_on
lift_comp_of 📖mathematicalMulHom.comp
Magma.AssocQuotient
Semigroup.toMul
instSemigroup
DFunLike.coe
Equiv
MulHom
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
Equiv.symm_apply_apply
lift_comp_of' 📖mathematicalDFunLike.coe
Equiv
MulHom
Semigroup.toMul
Magma.AssocQuotient
instSemigroup
EquivLike.toFunLike
Equiv.instEquivLike
lift
MulHom.comp
of
Equiv.apply_symm_apply
lift_of 📖mathematicalDFunLike.coe
MulHom
Magma.AssocQuotient
Semigroup.toMul
instSemigroup
MulHom.funLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
lift_symm_apply 📖mathematicalDFunLike.coe
Equiv
MulHom
Magma.AssocQuotient
Semigroup.toMul
instSemigroup
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
lift
MulHom.comp
of
map_of 📖mathematicalDFunLike.coe
MulHom
Magma.AssocQuotient
Semigroup.toMul
instSemigroup
MulHom.funLike
map
of
quot_mk_assoc 📖mathematicalMagma.AssocRel
quot_mk_assoc_left 📖mathematicalMagma.AssocRel

(root)

Definitions

NameCategoryTheorems
FreeAddMagma 📖CompData
25 mathmath: FreeAddMagma.traverse_add, FreeAddMagma.traverse_eq, FreeAddMagma.toFreeAddSemigroup_comp_of, FreeAddMagma.add_bind, FreeAddMagma.lift_comp_of, FreeAddMagma.toFreeAddSemigroup_comp_map, FreeAddMagma.add_eq, FreeAddMagma.map_of, FreeAddMagma.map_pure, FreeAddMagma.lift_comp_of', FreeAddMagma.instLawfulMonad, FreeAddMagma.traverse_pure', FreeAddMagma.pure_seq, FreeAddMagma.traverse_add', FreeAddMagma.toFreeAddSemigroup_of, FreeAddMagma.toFreeAddSemigroup_map, FreeAddMagma.lift_symm_apply, FreeAddMagma.map_add', FreeAddMagma.hom_ext_iff, FreeAddMagma.add_seq, FreeAddMagma.lift_of, FreeAddMagma.length_toFreeAddSemigroup, FreeAddMagma.instLawfulTraversable, FreeAddMagma.pure_bind, FreeAddMagma.traverse_pure
FreeAddMagmaAssocQuotientEquiv 📖CompOp
FreeAddSemigroup 📖CompData
30 mathmath: FreeAddSemigroup.map_pure, FreeAddSemigroup.lift_comp_of, FreeAddSemigroup.add_seq, FreeAddSemigroup.lift_symm_apply, FreeAddSemigroup.pure_seq, FreeAddSemigroup.instLawfulMonad, FreeAddSemigroup.mk_add_mk, FreeAddMagma.toFreeAddSemigroup_comp_of, FreeAddSemigroup.lift_of, FreeAddMagma.toFreeAddSemigroup_comp_map, FreeAddSemigroup.length_add, FreeAddSemigroup.traverse_pure', FreeAddSemigroup.map_add', FreeAddSemigroup.traverse_add, FreeAddSemigroup.length_map, FreeAddSemigroup.traverse_add', FreeAddSemigroup.map_of, FreeAddMagma.toFreeAddSemigroup_of, FreeAddMagma.toFreeAddSemigroup_map, FreeAddSemigroup.tail_add, FreeAddSemigroup.traverse_pure, FreeAddSemigroup.pure_bind, FreeAddSemigroup.add_bind, FreeAddSemigroup.hom_ext_iff, FreeAddMagma.length_toFreeAddSemigroup, FreeAddSemigroup.lift_of_add, FreeAddSemigroup.lift_comp_of', FreeAddSemigroup.head_add, FreeAddSemigroup.traverse_eq, FreeAddSemigroup.instLawfulTraversable
FreeMagma 📖CompData
40 mathmath: FreeMagma.lift_of, FreeMagma.toFreeSemigroup_of, FreeMagma.traverse_mul, FreeNonUnitalNonAssocAlgebra.of_comp_lift, FreeMagma.hom_ext_iff, FreeLieAlgebra.Rel.addLeft, FreeNonUnitalNonAssocAlgebra.lift_unique, FreeMagma.instLawfulTraversable, FreeMagma.map_mul', FreeLieAlgebra.liftAux_map_smul, FreeMagma.pure_seq, FreeLieAlgebra.liftAux_map_add, FreeNonUnitalNonAssocAlgebra.lift_symm_apply, FreeLieAlgebra.liftAux_map_mul, FreeMagma.instLawfulMonad, FreeLieAlgebra.liftAux_spec, FreeMagma.map_pure, FreeLieAlgebra.Rel.neg, FreeMagma.pure_bind, FreeLieAlgebra.Rel.subRight, FreeMagma.lift_symm_apply, FreeMagma.toFreeSemigroup_map, FreeMagma.toFreeSemigroup_comp_of, FreeMagma.lift_comp_of, FreeLieAlgebra.Rel.subLeft, FreeLieAlgebra.Rel.smulOfTower, FreeMagma.length_toFreeSemigroup, FreeMagma.map_of, FreeMagma.traverse_pure, FreeMagma.mul_bind, FreeMagma.traverse_mul', FreeMagma.traverse_eq, FreeMagma.mul_eq, FreeMagma.lift_comp_of', FreeMagma.toFreeSemigroup_comp_map, FreeNonUnitalNonAssocAlgebra.lift_of_apply, FreeMagma.mul_seq, FreeNonUnitalNonAssocAlgebra.hom_ext_iff, FreeMagma.traverse_pure', FreeNonUnitalNonAssocAlgebra.lift_comp_of
FreeMagmaAssocQuotientEquiv 📖CompOp
FreeSemigroup 📖CompData
30 mathmath: FreeSemigroup.traverse_pure', FreeMagma.toFreeSemigroup_of, FreeSemigroup.mul_bind, FreeSemigroup.head_mul, FreeSemigroup.tail_mul, FreeSemigroup.instLawfulTraversable, FreeSemigroup.map_pure, FreeSemigroup.traverse_mul', FreeSemigroup.mul_seq, FreeSemigroup.traverse_mul, FreeSemigroup.traverse_pure, FreeSemigroup.lift_symm_apply, FreeSemigroup.mk_mul_mk, FreeSemigroup.instLawfulMonad, FreeSemigroup.length_mul, FreeSemigroup.map_mul', FreeMagma.toFreeSemigroup_map, FreeSemigroup.lift_comp_of', FreeMagma.toFreeSemigroup_comp_of, FreeMagma.length_toFreeSemigroup, FreeSemigroup.traverse_eq, FreeMagma.toFreeSemigroup_comp_map, FreeSemigroup.length_map, FreeSemigroup.lift_of_mul, FreeSemigroup.hom_ext_iff, FreeSemigroup.lift_comp_of, FreeSemigroup.pure_bind, FreeSemigroup.pure_seq, FreeSemigroup.map_of, FreeSemigroup.lift_of
instDecidableEqFreeAddMagma 📖CompOp
instDecidableEqFreeMagma 📖CompOp
instReprFreeAddMagma 📖CompOp
instReprFreeMagma 📖CompOp

instDecidableEqFreeAddMagma

Definitions

NameCategoryTheorems
decEq 📖CompOp

instDecidableEqFreeMagma

Definitions

NameCategoryTheorems
decEq 📖CompOp

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