Documentation Verification Report

Basic

📁 Source: Mathlib/GroupTheory/FreeGroup/Basic.lean

Statistics

MetricCount
DefinitionsFreeAddGroup, IsReduced, aux, Red, Step, freeAddGroupCongr, freeAddGroupEmptyEquivAddUnit, instAdd, instAddGroup, instInhabited, instMonad, instNeg, instUniqueOfIsEmpty, instZero, map, mk, negRev, of, sum, FreeGroup, IsReduced, aux, Red, Step, freeGroupCongr, freeGroupEmptyEquivUnit, freeGroupUnitEquivInt, instGroup, instInhabited, instInv, instMonad, instMul, instOne, instUniqueOfIsEmpty, invRev, map, mk, of, prod, sum
40
Theoremsappend_overlap, infix, nil, not_step, of_forall_not_step, red_iff_eq, singleton, append_left, append_left_iff, append_right, cons, cons_cons_iff, cons_left_iff, cons_not, cons_not_rev, diamond, diamond_aux, length, negRev, not_rev, sublist, to_red, antisymm, append_append, append_append_left_iff, church_rosser, cons_cons, cons_cons_iff, cons_nil_iff_singleton, exact, length, length_le, negRev, neg_of_red_of_ne, nil_iff, not_step_nil, not_step_singleton, red_iff_addIrreducible, refl, singleton_iff, sizeof_of_step, step_negRev_iff, sublist, to_append_iff, trans, add_bind, add_mk, closure_eq_range, closure_range_of, equivalence_join_red, eqvGen_step_iff_join_red, ext_hom, ext_hom_iff, freeAddGroupCongr_apply, freeAddGroupCongr_refl, freeAddGroupCongr_symm, freeAddGroupCongr_trans, induction_on, instLawfulMonad, isReduced_cons_cons, isReduced_iff_not_step, join_red_of_step, lift_apply_of, lift_eq_sum_map, lift_mk, lift_of_apply, lift_of_eq_id, lift_symm_apply, lift_unique, comp, id, id', mk, of, unique, map_add, map_eq_lift, map_neg, map_pure, map_zero, negRev_append, negRev_bijective, negRev_cons, negRev_empty, negRev_injective, negRev_involutive, negRev_length, negRev_negRev, negRev_surjective, neg_bind, neg_mk, nsmul_mk, of_injective, pure_bind, quot_liftOn_mk, quot_lift_mk, quot_map_mk, quot_mk_eq_mk, range_lift_eq_closure, range_lift_le, red_negRev_iff, of, unique, sum_mk, zero_bind, zero_eq_mk, append_overlap, infix, nil, not_step, of_forall_not_step, red_iff_eq, singleton, append_left, append_left_iff, append_right, cons, cons_cons_iff, cons_left_iff, cons_not, cons_not_rev, diamond, diamond_aux, invRev, length, not_rev, sublist, to_red, antisymm, append_append, append_append_left_iff, church_rosser, cons_cons, cons_cons_iff, cons_nil_iff_singleton, exact, invRev, inv_of_red_of_ne, length, length_le, nil_iff, not_step_nil, not_step_singleton, red_iff_irreducible, refl, singleton_iff, sizeof_of_step, step_invRev_iff, sublist, to_append_iff, trans, closure_eq_range, closure_range_of, equivalence_join_red, eqvGen_step_iff_join_red, ext_hom, ext_hom_iff, freeGroupCongr_apply, freeGroupCongr_refl, freeGroupCongr_symm, freeGroupCongr_trans, induction_on, instLawfulMonad, invRev_append, invRev_bijective, invRev_cons, invRev_empty, invRev_injective, invRev_invRev, invRev_involutive, invRev_length, invRev_surjective, inv_bind, inv_mk, isReduced_cons_cons, isReduced_iff_not_step, join_red_of_step, lift_apply_of, lift_eq_prod_map, lift_mk, lift_of_apply, lift_of_eq_id, lift_symm_apply, lift_unique, comp, id, id', mk, of, unique, map_eq_lift, map_inv, map_mul, map_one, map_pure, mul_bind, mul_mk, of_injective, one_bind, one_eq_mk, pow_mk, of, unique, prod_mk, pure_bind, quot_liftOn_mk, quot_lift_mk, quot_map_mk, quot_mk_eq_mk, range_lift_eq_closure, range_lift_le, red_invRev_iff, map_inv, map_mul, map_one, of, sum_mk
217
Total257

FreeAddGroup

Definitions

NameCategoryTheorems
IsReduced 📖MathDef
11 mathmath: isReduced_cons_cons, IsCyclicallyReduced.isReduced, isReduced_iff_not_step, IsReduced.nil, IsReduced.of_reduce_eq, IsReduced.singleton, IsReduced.of_forall_not_step, isReduced_toWord, isCyclicallyReduced_iff, isCyclicallyReduced_cons_append_iff, isReduced_iff_reduce_eq
Red 📖MathDef
16 mathmath: Red.refl, Red.singleton_iff, join_red_of_step, IsReduced.red_iff_eq, Red.append_append_left_iff, Red.exact, Red.red_iff_addIrreducible, equivalence_join_red, Red.Step.to_red, red_negRev_iff, Red.to_append_iff, reduce.red, Red.nil_iff, eqvGen_step_iff_join_red, Red.cons_cons_iff, Red.cons_nil_iff_singleton
freeAddGroupCongr 📖CompOp
4 mathmath: freeAddGroupCongr_symm, freeAddGroupCongr_apply, freeAddGroupCongr_trans, freeAddGroupCongr_refl
freeAddGroupEmptyEquivAddUnit 📖CompOp
instAdd 📖CompOp
10 mathmath: freeAddGroupCongr_symm, add_bind, add_mk, toWord_add_sublist, freeAddGroupCongr_apply, freeAddGroupCongr_trans, norm_add_le, map_add, toWord_add, freeAddGroupCongr_refl
instAddGroup 📖CompOp
26 mathmath: map.id', instIsAddTorsionFree, toWord_of_nsmul, lift_mk, nsmul_mk, lift_apply_of, map.comp, map.id, closure_eq_range, ext_hom_iff, lift_of_eq_id, map_eq_lift, freeAddGroupCongr_apply, closure_range_of, sum_mk, AddGroup.fg_iff_exists_freeAddGroup_hom_surjective, map.mk, range_lift_le, lift_symm_apply, lift_eq_sum_map, lift_of_apply, map.of, sum.of, toWord_nsmul, range_lift_eq_closure, norm_of_nsmul
instInhabited 📖CompOp
instMonad 📖CompOp
9 mathmath: neg_bind, add_bind, map_zero, zero_bind, map_add, map_pure, map_neg, pure_bind, instLawfulMonad
instNeg 📖CompOp
5 mathmath: neg_bind, neg_mk, norm_neg_eq, toWord_neg, map_neg
instUniqueOfIsEmpty 📖CompOp
instZero 📖CompOp
7 mathmath: norm_eq_zero, map_zero, zero_bind, norm_zero, zero_eq_mk, toWord_eq_nil_iff, toWord_zero
map 📖CompOp
9 mathmath: map.id', map.comp, map.id, map_eq_lift, freeAddGroupCongr_apply, map.unique, map.mk, lift_eq_sum_map, map.of
mk 📖CompOp
negRev 📖CompOp
20 mathmath: reduce_negRev_left_cancel, reduce_negRev, negRev_append, negRev_involutive, negRev_bijective, negRev_injective, neg_mk, Red.negRev, Red.Step.negRev, negRev_empty, negRev_negRev, toWord_neg, reduceCyclically.conj_conjugator_reduceCyclically, red_negRev_iff, negRev_surjective, negRev_cons, reduceCyclically.reduce_flatten_replicate, reduceCyclically.reduce_flatten_replicate_succ, negRev_length, Red.step_negRev_iff
of 📖CompOp
14 mathmath: toWord_of_nsmul, toWord_of, norm_of, lift_apply_of, ext_hom_iff, lift_of_eq_id, map_eq_lift, of_injective, closure_range_of, lift_symm_apply, lift_of_apply, map.of, sum.of, norm_of_nsmul
sum 📖CompOp
4 mathmath: sum.unique, sum_mk, lift_eq_sum_map, sum.of

Theorems

NameKindAssumesProvesValidatesDepends On
add_bind 📖mathematicalFreeAddGroup
instMonad
instAdd
AddMonoidHom.map_add
add_mk 📖mathematicalFreeAddGroup
instAdd
closure_eq_range 📖mathematicalAddSubgroup.closure
AddMonoidHom.range
FreeAddGroup
Set
Set.instMembership
instAddGroup
DFunLike.coe
Equiv
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
EquivLike.toFunLike
Equiv.instEquivLike
lift
range_lift_eq_closure
Subtype.range_coe
closure_range_of 📖mathematicalAddSubgroup.closure
FreeAddGroup
instAddGroup
Set.range
of
Top.top
AddSubgroup
AddSubgroup.instTop
range_lift_eq_closure
lift_of_eq_id
AddMonoidHom.range_eq_top
equivalence_join_red 📖mathematicalRelation.Join
Red
Relation.equivalence_join_reflTransGen
Red.Step.diamond
Relation.ReflTransGen.single
eqvGen_step_iff_join_red 📖mathematicalRelation.EqvGen
Red.Step
Relation.Join
Red
Relation.EqvGen.mono
join_red_of_step
Equivalence.eqvGen_iff
equivalence_join_red
Relation.join_of_equivalence
Relation.EqvGen.is_equivalence
Relation.reflTransGen_of_equivalence
ext_hom 📖DFunLike.coe
AddMonoidHom
FreeAddGroup
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instAddGroup
AddMonoidHom.instFunLike
of
AddMonoidHom.ext
add_assoc
map_add
AddMonoidHomClass.toAddHomClass
AddMonoidHom.instAddMonoidHomClass
add_neg_cancel
map_zero
AddMonoidHomClass.toZeroHomClass
add_zero
neg_add_cancel
zero_add
induction_on
ext_hom_iff 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddGroup
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instAddGroup
AddMonoidHom.instFunLike
of
ext_hom
freeAddGroupCongr_apply 📖mathematicalDFunLike.coe
AddEquiv
FreeAddGroup
instAdd
EquivLike.toFunLike
AddEquiv.instEquivLike
freeAddGroupCongr
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instAddGroup
AddMonoidHom.instFunLike
map
Equiv
Equiv.instEquivLike
freeAddGroupCongr_refl 📖mathematicalfreeAddGroupCongr
Equiv.refl
AddEquiv.refl
FreeAddGroup
instAdd
AddEquiv.ext
map.id
freeAddGroupCongr_symm 📖mathematicalAddEquiv.symm
FreeAddGroup
instAdd
freeAddGroupCongr
Equiv.symm
freeAddGroupCongr_trans 📖mathematicalAddEquiv.trans
FreeAddGroup
instAdd
freeAddGroupCongr
Equiv.trans
AddEquiv.ext
map.comp
induction_on 📖FreeAddGroup
instZero
of
instNeg
instAdd
instLawfulMonad 📖mathematicalFreeAddGroup
instMonad
induction_on
map_zero
map_pure
map_neg
map_add
pure_bind
zero_bind
lift_apply_of
neg_bind
add_bind
isReduced_cons_cons 📖mathematicalIsReduced
isReduced_iff_not_step 📖mathematicalIsReduced
Red.Step
IsReduced.not_step
IsReduced.of_forall_not_step
join_red_of_step 📖mathematicalRed.StepRelation.Join
Red
Relation.join_of_single
Relation.reflexive_reflTransGen
Red.Step.to_red
lift_apply_of 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddGroup
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instAddGroup
AddMonoidHom.instFunLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
add_zero
lift_eq_sum_map 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddGroup
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instAddGroup
AddMonoidHom.instFunLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
sum
map
lift_unique
sum.of
AddMonoidHom.coe_comp
lift_mk 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddGroup
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instAddGroup
AddMonoidHom.instFunLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
AddZero.toAdd
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
NegZeroClass.toNeg
lift_of_apply 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddGroup
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instAddGroup
AddMonoidHom.instFunLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
DFunLike.congr_fun
lift_of_eq_id
lift_of_eq_id 📖mathematicalDFunLike.coe
Equiv
AddMonoidHom
FreeAddGroup
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instAddGroup
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
AddMonoidHom.id
Equiv.apply_symm_apply
lift_symm_apply 📖mathematicalDFunLike.coe
Equiv
AddMonoidHom
FreeAddGroup
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instAddGroup
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
lift
AddMonoidHom.instFunLike
of
lift_unique 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddGroup
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instAddGroup
AddMonoidHom.instFunLike
of
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
DFunLike.congr_fun
Equiv.symm_apply_eq
map_add 📖mathematicalFreeAddGroup
instMonad
instAdd
AddMonoidHom.map_add
map_eq_lift 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddGroup
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instAddGroup
AddMonoidHom.instFunLike
map
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
map.unique
lift_apply_of
map_neg 📖mathematicalFreeAddGroup
instMonad
instNeg
AddMonoidHom.map_neg
map_pure 📖mathematicalFreeAddGroup
instMonad
map.of
map_zero 📖mathematicalFreeAddGroup
instMonad
instZero
AddMonoidHom.map_zero
negRev_append 📖mathematicalnegRev
negRev_bijective 📖mathematicalFunction.Bijective
negRev
Function.Involutive.bijective
negRev_involutive
negRev_cons 📖mathematicalnegRev
negRev_empty 📖mathematicalnegRev
negRev_injective 📖mathematicalnegRevFunction.Involutive.injective
negRev_involutive
negRev_involutive 📖mathematicalFunction.Involutive
negRev
negRev_negRev
negRev_length 📖mathematicalnegRev
negRev_negRev 📖mathematicalnegRev
negRev_surjective 📖mathematicalnegRevFunction.Involutive.surjective
negRev_involutive
neg_bind 📖mathematicalFreeAddGroup
instMonad
instNeg
AddMonoidHom.map_neg
neg_mk 📖mathematicalFreeAddGroup
instNeg
negRev
nsmul_mk 📖mathematicalFreeAddGroup
AddMonoid.toNatSMul
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instAddGroup
succ_nsmul'
of_injective 📖mathematicalFreeAddGroup
of
Red.exact
Red.singleton_iff
pure_bind 📖mathematicalFreeAddGroup
instMonad
lift_apply_of
quot_liftOn_mk 📖mathematicalRed.Step
quot_lift_mk 📖mathematicalRed.Step
quot_map_mk 📖mathematicalRelator.LiftFun
Red.Step
Quot.map
quot_mk_eq_mk 📖mathematicalRed.Step
range_lift_eq_closure 📖mathematicalAddMonoidHom.range
FreeAddGroup
instAddGroup
DFunLike.coe
Equiv
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
EquivLike.toFunLike
Equiv.instEquivLike
lift
AddSubgroup.closure
Set.range
le_antisymm
range_lift_le
AddSubgroup.subset_closure
AddSubgroup.closure_le
lift_apply_of
range_lift_le 📖mathematicalSet
Set.instHasSubset
Set.range
SetLike.coe
AddSubgroup
AddSubgroup.instSetLike
Preorder.toLE
PartialOrder.toPreorder
AddSubgroup.instPartialOrder
AddMonoidHom.range
FreeAddGroup
instAddGroup
DFunLike.coe
Equiv
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
EquivLike.toFunLike
Equiv.instEquivLike
lift
AddSubgroup.zero_mem
AddSubgroup.add_mem
AddSubgroup.neg_mem
red_negRev_iff 📖mathematicalRed
negRev
negRev_negRev
Red.negRev
sum_mk 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddGroup
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
instAddGroup
AddMonoidHom.instFunLike
sum
AddZero.toAdd
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
NegZeroClass.toNeg
zero_bind 📖mathematicalFreeAddGroup
instMonad
instZero
AddMonoidHom.map_zero
zero_eq_mk 📖mathematicalFreeAddGroup
instZero

FreeAddGroup.IsReduced

Theorems

NameKindAssumesProvesValidatesDepends On
append_overlap 📖FreeAddGroup.IsReducedList.IsChain.append_overlap
infix 📖FreeAddGroup.IsReducedList.IsChain.infix
nil 📖mathematicalFreeAddGroup.IsReducedList.isChain_nil
not_step 📖mathematicalFreeAddGroup.IsReducedFreeAddGroup.Red.StepList.isChain_append_cons_cons
of_forall_not_step 📖mathematicalFreeAddGroup.Red.StepFreeAddGroup.IsReducednil
singleton
FreeAddGroup.isReduced_cons_cons
Bool.ne_not
FreeAddGroup.Red.Step.cons
red_iff_eq 📖mathematicalFreeAddGroup.IsReducedFreeAddGroup.RedRelation.reflTransGen_iff_eq
not_step
singleton 📖mathematicalFreeAddGroup.IsReducedList.isChain_singleton

FreeAddGroup.Lift

Definitions

NameCategoryTheorems
aux 📖CompOp
1 mathmath: FreeAddGroup.Red.Step.lift

FreeAddGroup.Red

Definitions

NameCategoryTheorems
Step 📖CompData
16 mathmath: Step.cons_not, FreeAddGroup.IsReduced.not_step, Step.cons_cons_iff, Step.append_left_iff, Step.diamond_aux, FreeAddGroup.isReduced_iff_not_step, Step.cons_not_rev, Step.not_rev, not_step_singleton, FreeAddGroup.quot_lift_mk, FreeAddGroup.quot_liftOn_mk, Step.cons_left_iff, FreeAddGroup.eqvGen_step_iff_join_red, not_step_nil, FreeAddGroup.quot_mk_eq_mk, step_negRev_iff

Theorems

NameKindAssumesProvesValidatesDepends On
antisymm 📖FreeAddGroup.RedList.Sublist.antisymm
sublist
append_append 📖FreeAddGroup.RedRelation.ReflTransGen.trans
Relation.ReflTransGen.lift
Step.append_right
append_append_left_iff
append_append_left_iff 📖mathematicalFreeAddGroup.Redcons_cons_iff
church_rosser 📖mathematicalFreeAddGroup.RedRelation.JoinRelation.church_rosser
Step.diamond
Step.to_red
cons_cons 📖FreeAddGroup.RedRelation.ReflTransGen.lift
Step.cons
cons_cons_iff 📖mathematicalFreeAddGroup.RedRelation.ReflTransGen.head_induction_on
Step.cons_left_iff
Relation.ReflTransGen.head
cons_cons
Step.cons_not_rev
cons_nil_iff_singleton 📖mathematicalFreeAddGroup.Redcons_cons
Relation.ReflTransGen.single
Step.cons_not_rev
church_rosser
singleton_iff
Step.cons_not
exact 📖mathematicalRelation.Join
FreeAddGroup.Red
Quot.eqvGen_exact
Quot.eqvGen_sound
FreeAddGroup.eqvGen_step_iff_join_red
length 📖FreeAddGroup.RedStep.length
add_assoc
mul_one
length_le 📖FreeAddGroup.Redsublist
negRev 📖mathematicalFreeAddGroup.RedFreeAddGroup.negRevRelation.ReflTransGen.lift
Step.negRev
neg_of_red_of_ne 📖FreeAddGroup.Redto_append_iff
nil_iff
append_append
cons_cons
Step.to_red
Step.cons_not_rev
church_rosser
red_iff_addIrreducible
nil_iff 📖mathematicalFreeAddGroup.RedRelation.reflTransGen_iff_eq
not_step_nil
not_step_nil 📖mathematicalStep
not_step_singleton 📖mathematicalStepStep.cons_left_iff
not_step_nil
red_iff_addIrreducible 📖mathematicalFreeAddGroup.RedRelation.reflTransGen_iff_eq
refl 📖mathematicalFreeAddGroup.Red
singleton_iff 📖mathematicalFreeAddGroup.RedRelation.reflTransGen_iff_eq
not_step_singleton
sizeof_of_step 📖Step
step_negRev_iff 📖mathematicalStep
FreeAddGroup.negRev
FreeAddGroup.negRev_negRev
Step.negRev
sublist 📖FreeAddGroup.RedRelation.reflTransGen_of_transitive_reflexive
Step.sublist
to_append_iff 📖mathematicalFreeAddGroup.Redrefl
append_append
trans 📖FreeAddGroup.RedRelation.ReflTransGen.trans

FreeAddGroup.Red.Step

Theorems

NameKindAssumesProvesValidatesDepends On
append_left 📖FreeAddGroup.Red.Step
append_left_iff 📖mathematicalFreeAddGroup.Red.Stepcons_cons_iff
append_right 📖FreeAddGroup.Red.Step
cons 📖FreeAddGroup.Red.Stepappend_left
cons_cons_iff 📖mathematicalFreeAddGroup.Red.Stepcons_left_iff
cons_left_iff 📖mathematicalFreeAddGroup.Red.Stepcons
cons_not
cons_not 📖mathematicalFreeAddGroup.Red.Step
cons_not_rev 📖mathematicalFreeAddGroup.Red.Stepnot_rev
diamond 📖FreeAddGroup.Red.Stepdiamond_aux
diamond_aux 📖mathematicalFreeAddGroup.Red.Stepcons_not
cons
length 📖FreeAddGroup.Red.Step
negRev 📖mathematicalFreeAddGroup.Red.StepFreeAddGroup.negRev
not_rev 📖mathematicalFreeAddGroup.Red.Step
sublist 📖FreeAddGroup.Red.Step
to_red 📖mathematicalFreeAddGroup.Red.StepFreeAddGroup.RedRelation.ReflTransGen.single

FreeAddGroup.map

Theorems

NameKindAssumesProvesValidatesDepends On
comp 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddGroup
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
FreeAddGroup.instAddGroup
AddMonoidHom.instFunLike
FreeAddGroup.map
id 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddGroup
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
FreeAddGroup.instAddGroup
AddMonoidHom.instFunLike
FreeAddGroup.map
id' 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddGroup
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
FreeAddGroup.instAddGroup
AddMonoidHom.instFunLike
FreeAddGroup.map
id
mk 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddGroup
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
FreeAddGroup.instAddGroup
AddMonoidHom.instFunLike
FreeAddGroup.map
of 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddGroup
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
FreeAddGroup.instAddGroup
AddMonoidHom.instFunLike
FreeAddGroup.map
FreeAddGroup.of
unique 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddGroup
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
FreeAddGroup.instAddGroup
AddMonoidHom.instFunLike
FreeAddGroup.of
FreeAddGroup.mapAddMonoidHom.map_zero
AddMonoidHom.map_add
AddMonoidHom.map_neg
map_add
AddMonoidHomClass.toAddHomClass
AddMonoidHom.instAddMonoidHomClass
map_neg

FreeAddGroup.sum

Theorems

NameKindAssumesProvesValidatesDepends On
of 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddGroup
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
FreeAddGroup.instAddGroup
AddMonoidHom.instFunLike
FreeAddGroup.sum
FreeAddGroup.of
FreeAddGroup.lift_apply_of
unique 📖mathematicalDFunLike.coe
AddMonoidHom
FreeAddGroup
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
FreeAddGroup.instAddGroup
AddMonoidHom.instFunLike
FreeAddGroup.of
FreeAddGroup.sumFreeAddGroup.lift_unique

FreeGroup

Definitions

NameCategoryTheorems
IsReduced 📖MathDef
11 mathmath: IsCyclicallyReduced.isReduced, IsReduced.nil, isCyclicallyReduced_cons_append_iff, isReduced_iff_not_step, isCyclicallyReduced_iff, isReduced_iff_reduce_eq, IsReduced.of_forall_not_step, isReduced_cons_cons, isReduced_toWord, IsReduced.of_reduce_eq, IsReduced.singleton
Red 📖MathDef
16 mathmath: join_red_of_step, Red.to_append_iff, Red.nil_iff, Red.Step.to_red, Red.cons_cons_iff, red_invRev_iff, Red.cons_nil_iff_singleton, Red.append_append_left_iff, equivalence_join_red, Red.singleton_iff, Red.exact, reduce.red, Red.refl, Red.red_iff_irreducible, IsReduced.red_iff_eq, eqvGen_step_iff_join_red
freeGroupCongr 📖CompOp
7 mathmath: CoxeterMatrix.reindex_relationsSet, freeGroupCongr_trans, freeGroupCongr_refl, PresentedGroup.equivPresentedGroup_symm_apply_of, freeGroupCongr_apply, freeGroupCongr_symm, PresentedGroup.equivPresentedGroup_apply_of
freeGroupEmptyEquivUnit 📖CompOp
freeGroupUnitEquivInt 📖CompOp
instGroup 📖CompOp
42 mathmath: prod.of, PresentedGroup.mk_eq_mk_of_mul_inv_mem, ext_hom_iff, lift_of_eq_id, closure_range_of, FreeGroupBasis.instIsFreeGroupFreeGroup, lift_apply_of, norm_of_pow, toWord_of_pow, map.mk, FreeAbelianGroup.liftAddEquiv_symm_apply, FreeGroupBasis.lift_apply_apply, toWord_pow, injective_lift_of_ping_pong, map.id', map.comp, lift_symm_apply, instIsMulTorsionFree, range_lift_eq_closure, PresentedGroup.mk_eq_one_iff, PresentedGroup.mk_eq_mk_of_inv_mul_mem, closure_eq_range, freeGroupEquivCoprodI_symm_apply, pow_mk, PresentedGroup.mk_surjective, prod_mk, PresentedGroup.one_of_mem, map.of, startsWith.smul_def, FreeGroupBasis.lift_symm_apply, FreeGroupBasis.ofFreeGroup_apply, map.id, Orbit.duplicate, freeGroupEquivCoprodI_apply, FreeAbelianGroup.liftAddEquiv_apply_apply, Group.fg_iff_exists_freeGroup_hom_surjective, freeGroupCongr_apply, lift_mk, lift_eq_prod_map, range_lift_le, map_eq_lift, lift_of_apply
instInhabited 📖CompOp
instInv 📖CompOp
7 mathmath: inv_bind, toWord_inv, inv_mk, Orbit.duplicate, map_inv, norm_inv_eq, sum.map_inv
instMonad 📖CompOp
9 mathmath: pure_bind, instLawfulMonad, mul_bind, one_bind, inv_bind, map_mul, map_one, map_pure, map_inv
instMul 📖CompOp
22 mathmath: FreeGroupBasis.repr_apply_coe, CoxeterMatrix.reindex_relationsSet, freeGroupCongr_trans, freeGroupCongr_refl, norm_mul_le, startsWith_mk_mul, toWord_mul_sublist, mul_bind, IsFreeGroup.mulEquiv_def, IsFreeGroup.toFreeGroup_symm_apply, map_mul, freeGroupEquivCoprodI_symm_apply, sum.map_mul, IsFreeGroup.toFreeGroup_apply, mul_mk, FreeGroupBasis.lift_symm_apply, PresentedGroup.equivPresentedGroup_symm_apply_of, freeGroupEquivCoprodI_apply, freeGroupCongr_apply, freeGroupCongr_symm, toWord_mul, PresentedGroup.equivPresentedGroup_apply_of
instOne 📖CompOp
8 mathmath: sum.map_one, one_bind, norm_one, toWord_one, one_eq_mk, map_one, norm_eq_zero, toWord_eq_nil_iff
instUniqueOfIsEmpty 📖CompOp
invRev 📖CompOp
20 mathmath: invRev_cons, reduce_invRev_left_cancel, invRev_empty, invRev_length, reduceCyclically.reduce_flatten_replicate_succ, red_invRev_iff, invRev_involutive, invRev_bijective, invRev_invRev, invRev_injective, toWord_inv, invRev_surjective, Red.step_invRev_iff, reduceCyclically.conj_conjugator_reduceCyclically, Red.Step.invRev, Red.invRev, inv_mk, invRev_append, reduce_invRev, reduceCyclically.reduce_flatten_replicate
map 📖CompOp
9 mathmath: map.mk, map.id', map.comp, map.of, map.unique, map.id, freeGroupCongr_apply, lift_eq_prod_map, map_eq_lift
mk 📖CompOp
of 📖CompOp
21 mathmath: FreeGroupBasis.repr_apply_coe, prod.of, ext_hom_iff, lift_of_eq_id, closure_range_of, lift_apply_of, norm_of_pow, toWord_of_pow, FreeAbelianGroup.liftAddEquiv_symm_apply, sum.of, lift_symm_apply, freeGroupEquivCoprodI_symm_apply, toWord_of, map.of, norm_of, FreeGroupBasis.lift_symm_apply, FreeGroupBasis.ofFreeGroup_apply, of_injective, freeGroupEquivCoprodI_apply, map_eq_lift, lift_of_apply
prod 📖CompOp
4 mathmath: prod.of, prod_mk, prod.unique, lift_eq_prod_map
sum 📖CompOp
5 mathmath: sum_mk, sum.map_one, sum.of, sum.map_mul, sum.map_inv

Theorems

NameKindAssumesProvesValidatesDepends On
closure_eq_range 📖mathematicalSubgroup.closure
MonoidHom.range
FreeGroup
Set
Set.instMembership
instGroup
DFunLike.coe
Equiv
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
EquivLike.toFunLike
Equiv.instEquivLike
lift
range_lift_eq_closure
Subtype.range_coe
closure_range_of 📖mathematicalSubgroup.closure
FreeGroup
instGroup
Set.range
of
Top.top
Subgroup
Subgroup.instTop
range_lift_eq_closure
lift_of_eq_id
MonoidHom.range_eq_top
equivalence_join_red 📖mathematicalRelation.Join
Red
Relation.equivalence_join_reflTransGen
Red.Step.diamond
Relation.ReflTransGen.single
eqvGen_step_iff_join_red 📖mathematicalRelation.EqvGen
Red.Step
Relation.Join
Red
Relation.EqvGen.mono
join_red_of_step
Equivalence.eqvGen_iff
equivalence_join_red
Relation.join_of_equivalence
Relation.EqvGen.is_equivalence
Relation.reflTransGen_of_equivalence
ext_hom 📖DFunLike.coe
MonoidHom
FreeGroup
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instGroup
MonoidHom.instFunLike
of
MonoidHom.ext
mul_assoc
MonoidHomClass.toMulHomClass
MonoidHom.instMonoidHomClass
mul_inv_cancel
map_one
MonoidHomClass.toOneHomClass
mul_one
inv_mul_cancel
one_mul
induction_on
map_mul
ext_hom_iff 📖mathematicalDFunLike.coe
MonoidHom
FreeGroup
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instGroup
MonoidHom.instFunLike
of
ext_hom
freeGroupCongr_apply 📖mathematicalDFunLike.coe
MulEquiv
FreeGroup
instMul
EquivLike.toFunLike
MulEquiv.instEquivLike
freeGroupCongr
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instGroup
MonoidHom.instFunLike
map
Equiv
Equiv.instEquivLike
freeGroupCongr_refl 📖mathematicalfreeGroupCongr
Equiv.refl
MulEquiv.refl
FreeGroup
instMul
MulEquiv.ext
map.id
freeGroupCongr_symm 📖mathematicalMulEquiv.symm
FreeGroup
instMul
freeGroupCongr
Equiv.symm
freeGroupCongr_trans 📖mathematicalMulEquiv.trans
FreeGroup
instMul
freeGroupCongr
Equiv.trans
MulEquiv.ext
map.comp
induction_on 📖FreeGroup
instOne
of
instInv
instMul
instLawfulMonad 📖mathematicalFreeGroup
instMonad
induction_on
map_one
map_pure
map_inv
map_mul
pure_bind
one_bind
lift_apply_of
inv_bind
mul_bind
invRev_append 📖mathematicalinvRev
invRev_bijective 📖mathematicalFunction.Bijective
invRev
Function.Involutive.bijective
invRev_involutive
invRev_cons 📖mathematicalinvRev
invRev_empty 📖mathematicalinvRev
invRev_injective 📖mathematicalinvRevFunction.Involutive.injective
invRev_involutive
invRev_invRev 📖mathematicalinvRev
invRev_involutive 📖mathematicalFunction.Involutive
invRev
invRev_invRev
invRev_length 📖mathematicalinvRev
invRev_surjective 📖mathematicalinvRevFunction.Involutive.surjective
invRev_involutive
inv_bind 📖mathematicalFreeGroup
instMonad
instInv
MonoidHom.map_inv
inv_mk 📖mathematicalFreeGroup
instInv
invRev
isReduced_cons_cons 📖mathematicalIsReduced
isReduced_iff_not_step 📖mathematicalIsReduced
Red.Step
IsReduced.not_step
IsReduced.of_forall_not_step
join_red_of_step 📖mathematicalRed.StepRelation.Join
Red
Relation.join_of_single
Relation.reflexive_reflTransGen
Red.Step.to_red
lift_apply_of 📖mathematicalDFunLike.coe
MonoidHom
FreeGroup
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instGroup
MonoidHom.instFunLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
mul_one
lift_eq_prod_map 📖mathematicalDFunLike.coe
MonoidHom
FreeGroup
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instGroup
MonoidHom.instFunLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
prod
map
lift_unique
prod.of
MonoidHom.coe_comp
lift_mk 📖mathematicalDFunLike.coe
MonoidHom
FreeGroup
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instGroup
MonoidHom.instFunLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
MulOne.toMul
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
InvOneClass.toInv
lift_of_apply 📖mathematicalDFunLike.coe
MonoidHom
FreeGroup
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instGroup
MonoidHom.instFunLike
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
DFunLike.congr_fun
lift_of_eq_id
lift_of_eq_id 📖mathematicalDFunLike.coe
Equiv
MonoidHom
FreeGroup
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instGroup
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
MonoidHom.id
Equiv.apply_symm_apply
lift_symm_apply 📖mathematicalDFunLike.coe
Equiv
MonoidHom
FreeGroup
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instGroup
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
lift
MonoidHom.instFunLike
of
lift_unique 📖mathematicalDFunLike.coe
MonoidHom
FreeGroup
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instGroup
MonoidHom.instFunLike
of
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
DFunLike.congr_fun
Equiv.symm_apply_eq
map_eq_lift 📖mathematicalDFunLike.coe
MonoidHom
FreeGroup
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instGroup
MonoidHom.instFunLike
map
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
lift
of
map.unique
lift_apply_of
map_inv 📖mathematicalFreeGroup
instMonad
instInv
MonoidHom.map_inv
map_mul 📖mathematicalFreeGroup
instMonad
instMul
MonoidHom.map_mul
map_one 📖mathematicalFreeGroup
instMonad
instOne
MonoidHom.map_one
map_pure 📖mathematicalFreeGroup
instMonad
map.of
mul_bind 📖mathematicalFreeGroup
instMonad
instMul
MonoidHom.map_mul
mul_mk 📖mathematicalFreeGroup
instMul
of_injective 📖mathematicalFreeGroup
of
Red.exact
one_bind 📖mathematicalFreeGroup
instMonad
instOne
MonoidHom.map_one
one_eq_mk 📖mathematicalFreeGroup
instOne
pow_mk 📖mathematicalFreeGroup
Monoid.toNatPow
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instGroup
pow_succ'
prod_mk 📖mathematicalDFunLike.coe
MonoidHom
FreeGroup
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instGroup
MonoidHom.instFunLike
prod
MulOne.toMul
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
InvOneClass.toInv
pure_bind 📖mathematicalFreeGroup
instMonad
lift_apply_of
quot_liftOn_mk 📖mathematicalRed.Step
quot_lift_mk 📖mathematicalRed.Step
quot_map_mk 📖mathematicalRelator.LiftFun
Red.Step
Quot.map
quot_mk_eq_mk 📖mathematicalRed.Step
range_lift_eq_closure 📖mathematicalMonoidHom.range
FreeGroup
instGroup
DFunLike.coe
Equiv
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
EquivLike.toFunLike
Equiv.instEquivLike
lift
Subgroup.closure
Set.range
le_antisymm
range_lift_le
Subgroup.subset_closure
Subgroup.closure_le
lift_apply_of
range_lift_le 📖mathematicalSet
Set.instHasSubset
Set.range
SetLike.coe
Subgroup
Subgroup.instSetLike
Preorder.toLE
PartialOrder.toPreorder
Subgroup.instPartialOrder
MonoidHom.range
FreeGroup
instGroup
DFunLike.coe
Equiv
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
EquivLike.toFunLike
Equiv.instEquivLike
lift
Subgroup.one_mem
Subgroup.mul_mem
Subgroup.inv_mem
red_invRev_iff 📖mathematicalRed
invRev
invRev_invRev
Red.invRev
sum_mk 📖mathematicalsum
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
NegZeroClass.toNeg

FreeGroup.IsReduced

Theorems

NameKindAssumesProvesValidatesDepends On
append_overlap 📖FreeGroup.IsReducedList.IsChain.append_overlap
infix 📖FreeGroup.IsReducedList.IsChain.infix
nil 📖mathematicalFreeGroup.IsReducedList.isChain_nil
not_step 📖mathematicalFreeGroup.IsReducedFreeGroup.Red.Step
of_forall_not_step 📖mathematicalFreeGroup.Red.StepFreeGroup.IsReducednil
singleton
FreeGroup.isReduced_cons_cons
Bool.ne_not
FreeGroup.Red.Step.cons
red_iff_eq 📖mathematicalFreeGroup.IsReducedFreeGroup.RedRelation.reflTransGen_iff_eq
not_step
singleton 📖mathematicalFreeGroup.IsReducedList.isChain_singleton

FreeGroup.Lift

Definitions

NameCategoryTheorems
aux 📖CompOp
1 mathmath: FreeGroup.Red.Step.lift

FreeGroup.Red

Definitions

NameCategoryTheorems
Step 📖CompData
16 mathmath: Step.cons_not, FreeGroup.isReduced_iff_not_step, FreeGroup.IsReduced.not_step, Step.not_rev, Step.cons_not_rev, not_step_nil, Step.diamond_aux, Step.cons_cons_iff, step_invRev_iff, not_step_singleton, FreeGroup.eqvGen_step_iff_join_red, Step.append_left_iff, Step.cons_left_iff, FreeGroup.quot_mk_eq_mk, FreeGroup.quot_liftOn_mk, FreeGroup.quot_lift_mk

Theorems

NameKindAssumesProvesValidatesDepends On
antisymm 📖FreeGroup.RedList.Sublist.antisymm
sublist
append_append 📖FreeGroup.RedRelation.ReflTransGen.trans
Relation.ReflTransGen.lift
Step.append_right
append_append_left_iff
append_append_left_iff 📖mathematicalFreeGroup.Red
church_rosser 📖mathematicalFreeGroup.RedRelation.JoinRelation.church_rosser
Step.diamond
Step.to_red
cons_cons 📖FreeGroup.RedRelation.ReflTransGen.lift
Step.cons
cons_cons_iff 📖mathematicalFreeGroup.RedRelation.ReflTransGen.head_induction_on
Step.cons_left_iff
Relation.ReflTransGen.head
cons_cons
Step.cons_not_rev
cons_nil_iff_singleton 📖mathematicalFreeGroup.Redcons_cons
Relation.ReflTransGen.single
Step.cons_not_rev
church_rosser
singleton_iff
Step.cons_not
exact 📖mathematicalRelation.Join
FreeGroup.Red
Quot.eqvGen_exact
Quot.eqvGen_sound
FreeGroup.eqvGen_step_iff_join_red
invRev 📖mathematicalFreeGroup.RedFreeGroup.invRevRelation.ReflTransGen.lift
Step.invRev
inv_of_red_of_ne 📖FreeGroup.Redto_append_iff
append_append
cons_cons
Step.to_red
Step.cons_not_rev
church_rosser
red_iff_irreducible
length 📖FreeGroup.RedStep.length
add_assoc
mul_one
length_le 📖FreeGroup.Redsublist
nil_iff 📖mathematicalFreeGroup.RedRelation.reflTransGen_iff_eq
not_step_nil
not_step_nil 📖mathematicalStep
not_step_singleton 📖mathematicalStep
red_iff_irreducible 📖mathematicalFreeGroup.RedRelation.reflTransGen_iff_eq
refl 📖mathematicalFreeGroup.Red
singleton_iff 📖mathematicalFreeGroup.RedRelation.reflTransGen_iff_eq
not_step_singleton
sizeof_of_step 📖Step
step_invRev_iff 📖mathematicalStep
FreeGroup.invRev
FreeGroup.invRev_invRev
Step.invRev
sublist 📖FreeGroup.RedRelation.reflTransGen_of_transitive_reflexive
Step.sublist
to_append_iff 📖mathematicalFreeGroup.Redrefl
append_append
trans 📖FreeGroup.RedRelation.ReflTransGen.trans

FreeGroup.Red.Step

Theorems

NameKindAssumesProvesValidatesDepends On
append_left 📖FreeGroup.Red.Step
append_left_iff 📖mathematicalFreeGroup.Red.Step
append_right 📖FreeGroup.Red.Step
cons 📖FreeGroup.Red.Stepappend_left
cons_cons_iff 📖mathematicalFreeGroup.Red.Step
cons_left_iff 📖mathematicalFreeGroup.Red.Stepcons
cons_not
cons_not 📖mathematicalFreeGroup.Red.Step
cons_not_rev 📖mathematicalFreeGroup.Red.Stepnot_rev
diamond 📖FreeGroup.Red.Stepdiamond_aux
diamond_aux 📖mathematicalFreeGroup.Red.Stepcons_not
cons
invRev 📖mathematicalFreeGroup.Red.StepFreeGroup.invRev
length 📖FreeGroup.Red.Step
not_rev 📖mathematicalFreeGroup.Red.Step
sublist 📖FreeGroup.Red.Step
to_red 📖mathematicalFreeGroup.Red.StepFreeGroup.RedRelation.ReflTransGen.single

FreeGroup.map

Theorems

NameKindAssumesProvesValidatesDepends On
comp 📖mathematicalDFunLike.coe
MonoidHom
FreeGroup
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
FreeGroup.instGroup
MonoidHom.instFunLike
FreeGroup.map
id 📖mathematicalDFunLike.coe
MonoidHom
FreeGroup
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
FreeGroup.instGroup
MonoidHom.instFunLike
FreeGroup.map
id' 📖mathematicalDFunLike.coe
MonoidHom
FreeGroup
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
FreeGroup.instGroup
MonoidHom.instFunLike
FreeGroup.map
id
mk 📖mathematicalDFunLike.coe
MonoidHom
FreeGroup
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
FreeGroup.instGroup
MonoidHom.instFunLike
FreeGroup.map
of 📖mathematicalDFunLike.coe
MonoidHom
FreeGroup
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
FreeGroup.instGroup
MonoidHom.instFunLike
FreeGroup.map
FreeGroup.of
unique 📖mathematicalDFunLike.coe
MonoidHom
FreeGroup
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
FreeGroup.instGroup
MonoidHom.instFunLike
FreeGroup.of
FreeGroup.mapMonoidHom.map_one
MonoidHom.map_mul
MonoidHom.map_inv
map_mul
MonoidHomClass.toMulHomClass
MonoidHom.instMonoidHomClass
map_inv

FreeGroup.prod

Theorems

NameKindAssumesProvesValidatesDepends On
of 📖mathematicalDFunLike.coe
MonoidHom
FreeGroup
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
FreeGroup.instGroup
MonoidHom.instFunLike
FreeGroup.prod
FreeGroup.of
FreeGroup.lift_apply_of
unique 📖mathematicalDFunLike.coe
MonoidHom
FreeGroup
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
FreeGroup.instGroup
MonoidHom.instFunLike
FreeGroup.of
FreeGroup.prodFreeGroup.lift_unique

FreeGroup.sum

Theorems

NameKindAssumesProvesValidatesDepends On
map_inv 📖mathematicalFreeGroup.sum
FreeGroup
FreeGroup.instInv
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
MonoidHom.map_inv
map_mul 📖mathematicalFreeGroup.sum
FreeGroup
FreeGroup.instMul
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
MonoidHom.map_mul
map_one 📖mathematicalFreeGroup.sum
FreeGroup
FreeGroup.instOne
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
MonoidHom.map_one
of 📖mathematicalFreeGroup.sum
FreeGroup.of
FreeGroup.prod.of

(root)

Definitions

NameCategoryTheorems
FreeAddGroup 📖CompOp
57 mathmath: FreeAddGroup.map.id', FreeAddGroup.neg_bind, FreeAddGroup.instIsAddTorsionFree, FreeAddGroup.freeAddGroupCongr_symm, FreeAddGroup.toWord_of_nsmul, FreeAddGroup.norm_surjective, FreeAddGroup.lift_mk, FreeAddGroup.nsmul_mk, FreeAddGroup.neg_mk, FreeAddGroup.add_bind, FreeAddGroup.lift_apply_of, FreeAddGroup.norm_eq_zero, FreeAddGroup.map.comp, FreeAddGroup.map_zero, FreeAddGroup.add_mk, FreeAddGroup.map.id, FreeAddGroup.closure_eq_range, Cardinal.mk_freeAddGroup, FreeAddGroup.ext_hom_iff, FreeAddGroup.toWord_add_sublist, FreeAddGroup.lift_of_eq_id, FreeAddGroup.toWord_injective, FreeAddGroup.norm_neg_eq, FreeAddGroup.zero_bind, FreeAddGroup.norm_zero, FreeAddGroup.zero_eq_mk, FreeAddGroup.map_eq_lift, instInfiniteFreeAddGroupOfNonempty, FreeAddGroup.freeAddGroupCongr_apply, FreeAddGroup.of_injective, FreeAddGroup.closure_range_of, FreeAddGroup.sum_mk, FreeAddGroup.freeAddGroupCongr_trans, FreeAddGroup.toWord_eq_nil_iff, FreeAddGroup.norm_add_le, FreeAddGroup.toWord_neg, AddGroup.fg_iff_exists_freeAddGroup_hom_surjective, FreeAddGroup.map.mk, FreeAddGroup.range_lift_le, FreeAddGroup.lift_symm_apply, FreeAddGroup.lift_eq_sum_map, FreeAddGroup.map_add, FreeAddGroup.lift_of_apply, FreeAddGroup.map_pure, FreeAddGroup.toWord_zero, FreeAddGroup.map.of, instCountableFreeAddGroup, FreeAddGroup.instNontrivialOfNonempty, FreeAddGroup.map_neg, FreeAddGroup.sum.of, FreeAddGroup.toWord_nsmul, FreeAddGroup.toWord_add, FreeAddGroup.pure_bind, FreeAddGroup.range_lift_eq_closure, FreeAddGroup.norm_of_nsmul, FreeAddGroup.instLawfulMonad, FreeAddGroup.freeAddGroupCongr_refl
FreeGroup 📖CompOp
82 mathmath: FreeGroup.norm_surjective, FreeGroupBasis.repr_apply_coe, FreeGroup.prod.of, CoxeterMatrix.reindex_relationsSet, FreeGroup.startsWith.Injective, FreeGroup.freeGroupCongr_trans, FreeGroup.ext_hom_iff, FreeGroup.lift_of_eq_id, FreeGroup.closure_range_of, FreeGroupBasis.instIsFreeGroupFreeGroup, FreeGroup.lift_apply_of, FreeGroup.norm_of_pow, FreeGroup.pure_bind, FreeGroup.instLawfulMonad, FreeGroup.toWord_of_pow, FreeGroup.freeGroupCongr_refl, FreeGroup.norm_mul_le, FreeGroup.map.mk, FreeAbelianGroup.liftAddEquiv_symm_apply, FreeGroupBasis.lift_apply_apply, FreeGroup.sum.map_one, FreeGroup.toWord_mul_sublist, FreeGroup.mul_bind, IsFreeGroup.mulEquiv_def, FreeGroup.one_bind, FreeGroup.toWord_pow, FreeGroup.injective_lift_of_ping_pong, FreeGroup.map.id', FreeGroup.map.comp, FreeGroup.lift_symm_apply, FreeGroup.instIsMulTorsionFree, FreeGroup.inv_bind, instCountableFreeGroup, IsFreeGroup.toFreeGroup_symm_apply, FreeGroup.map_mul, FreeGroup.range_lift_eq_closure, PresentedGroup.mk_eq_one_iff, FreeGroup.closure_eq_range, FreeGroup.norm_one, freeGroupEquivCoprodI_symm_apply, FreeGroup.toWord_inv, FreeGroup.pow_mk, FreeGroup.sum.map_mul, FreeGroup.toWord_one, PresentedGroup.mk_surjective, IsFreeGroup.toFreeGroup_apply, FreeGroup.one_eq_mk, FreeGroup.startsWith.disjoint_iff_ne, FreeGroup.prod_mk, Cardinal.mk_freeGroup, FreeGroup.mul_mk, FreeGroup.map.of, FreeGroup.startsWith.smul_def, FreeGroup.map_one, FreeGroup.toWord_injective, FreeGroupBasis.lift_symm_apply, FreeGroupBasis.ofFreeGroup_apply, FreeGroup.norm_eq_zero, FreeGroup.map.id, FreeGroup.of_injective, FreeGroup.instNontrivialOfNonempty, FreeGroup.inv_mk, PresentedGroup.equivPresentedGroup_symm_apply_of, FreeGroup.map_pure, FreeGroup.Orbit.duplicate, freeGroupEquivCoprodI_apply, FreeGroup.map_inv, FreeAbelianGroup.liftAddEquiv_apply_apply, Group.fg_iff_exists_freeGroup_hom_surjective, FreeGroup.norm_inv_eq, FreeGroup.freeGroupCongr_apply, FreeGroup.lift_mk, FreeGroup.lift_eq_prod_map, FreeGroup.freeGroupCongr_symm, FreeGroup.range_lift_le, FreeGroup.sum.map_inv, FreeGroup.toWord_mul, PresentedGroup.equivPresentedGroup_apply_of, FreeGroup.map_eq_lift, FreeGroup.lift_of_apply, instInfiniteFreeGroupOfNonempty, FreeGroup.toWord_eq_nil_iff

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