Documentation Verification Report

Operations

📁 Source: Mathlib/Combinatorics/SimpleGraph/Walks/Operations.lean

Statistics

MetricCount
Definitionsappend, concat, concatRec, concatRecAux, copy, drop, dropLast, reverse, reverseAux, tail, take
11
Theoremsappend, eq_copy_nil, tail, append_assoc, append_concat, append_copy_copy, append_nil, append_reverseAux, append_take_drop_eq, coe_support_append, coe_support_append', concatRec_concat, concatRec_nil, concat_append, concat_cons, concat_dropLast, concat_eq_append, concat_inj, concat_ne_nil, concat_nil, cons_append, cons_copy, cons_nil_append, cons_reverseAux, cons_support_tail, cons_tail_eq, copy_cons, copy_copy, copy_nil, copy_rfl_rfl, dart_snd_mem_support_of_mem_darts, darts_append, darts_concat, darts_copy, darts_drop, darts_reverse, darts_take, dropLast_concat, dropLast_cons_cons, dropLast_cons_nil, dropLast_cons_of_not_nil, dropLast_nil, drop_add_eq, drop_add_heq, drop_cons_eq, drop_getVert, drop_length, drop_of_length_le, drop_support_eq_support_drop_min, drop_zero, edgeSet_append, edgeSet_concat, edgeSet_copy, edgeSet_reverse, edges_append, edges_concat, edges_copy, edges_drop, edges_nodup_of_support_nodup, edges_reverse, edges_take, exists_concat_eq_cons, exists_cons_eq_concat, ext_getVert, ext_getVert_le_length, ext_support, fst_mem_support_of_mem_edges, getVert_append, getVert_copy, getVert_mem_tail_support, getVert_reverse, getVert_tail, length_append, length_concat, length_copy, length_reverse, length_reverseAux, length_tail_add_one, mem_darts_reverse, mem_support_append_iff, mem_support_of_mem_edges, mem_tail_support_append_iff, nil_append, nil_append_iff, nil_copy, nil_drop_iff, nil_drop_of_length_le, nil_reverse, nil_take_iff, nodup_tail_support_reverse, not_nil_of_tail_not_nil, penultimate_concat, penultimate_reverse, reverseAux_append, reverseAux_eq_reverse_append, reverse_append, reverse_bijective, reverse_concat, reverse_cons, reverse_copy, reverse_injective, reverse_nil, reverse_reverse, reverse_singleton, reverse_surjective, reverse_toWalk, snd_mem_support_of_mem_edges, snd_reverse, subset_support_append_left, subset_support_append_right, support_append, support_append_eq_support_dropLast_append, support_concat, support_copy, support_eq_concat, support_injective, support_reverse, support_subset_support_concat, support_tail, support_tail_of_not_nil, tail_cons, tail_cons_eq, tail_cons_nil, tail_nil, tail_support_append, take_add_eq, take_add_heq, take_cons_eq, take_getVert, take_length, take_of_length_le, take_support_eq_support_take_succ, take_zero
133
Total144

SimpleGraph.Walk

Definitions

NameCategoryTheorems
append 📖CompOp
41 mathmath: concat_eq_append, nil_append_iff, cons_append, reverse_append, getVert_append, cons_nil_append, subset_support_append_left, take_spec, append_take_drop_eq, append_copy_copy, coe_support_append, transfer_append, mem_support_iff_exists_append, append_reverseAux, mem_tail_support_append_iff, subset_support_append_right, append_assoc, length_append, take_add_heq, IsPath.mem_support_iff_exists_append, toSubgraph_append, support_append_eq_support_dropLast_append, support_append, reverseAux_append, Nil.append, darts_append, edges_append, edgeSet_append, takeUntil_append_of_mem_left, map_append, concat_append, reverse_cons, append_nil, tail_support_append, take_add_eq, nil_append, nil_isSubwalk_iff_exists, coe_support_append', append_concat, reverseAux_eq_reverse_append, mem_support_append_iff
concat 📖CompOp
24 mathmath: concat_eq_append, SimpleGraph.walkLengthTwoEquivCommonNeighbors_symm_apply_coe, edges_concat, concatRec_concat, penultimate_concat, darts_concat, exists_concat_eq_cons, isSubwalk_concat, concat_dropLast, IsPath.concat, edgeSet_concat, support_concat, length_concat, support_subset_support_concat, exists_cons_eq_concat, SimpleGraph.IsAcyclic.path_concat, concat_nil, concat_cons, dropLast_concat, IsSubwalk.concat, concat_append, append_concat, concat_isPath_iff, reverse_concat
concatRec 📖CompOp
2 mathmath: concatRec_concat, concatRec_nil
concatRecAux 📖CompOp
copy 📖CompOp
40 mathmath: edges_copy, nil_copy, copy_rfl_rfl, map_copy, take_zero, concat_inj, darts_copy, bypass_copy, drop_zero, IsSubwalk.copy, support_copy, tail_cons_eq, cons_copy, toDeleteEdges_copy, isCycle_copy, append_copy_copy, dropLast_cons_of_not_nil, edgeSet_copy, Nil.eq_copy_nil, take_of_length_le, reverse_copy, tail_cons, getVert_copy, isPath_copy, isTrail_copy, dropUntil_eq_drop, takeUntil_eq_take, length_copy, drop_add_eq, drop_of_length_le, copy_copy, isSubwalk_nil_iff, dropLast_concat, map_eq_of_eq, copy_nil, take_cons_eq, isCircuit_copy, take_add_eq, drop_cons_eq, copy_cons
drop 📖CompOp
18 mathmath: drop_zero, nil_drop_of_length_le, drop_isSubwalk_drop, isSubwalk_drop, append_take_drop_eq, darts_drop, nil_drop_iff, drop_add_heq, dropUntil_eq_drop, take_add_heq, drop_getVert, drop_length, edges_drop, drop_add_eq, drop_of_length_le, take_add_eq, drop_cons_eq, drop_support_eq_support_drop_min
dropLast 📖CompOp
7 mathmath: concat_dropLast, dropLast_cons_nil, dropLast_cons_of_not_nil, dropLast_nil, dropLast_cons_cons, dropLast_concat, IsSubwalk.dropLast
reverse 📖CompOp
33 mathmath: reverse_nil, reverse_toWalk, reverse_injective, toSubgraph_reverse, penultimate_reverse, reverse_surjective, getVert_reverse, edgeSet_reverse, reverse_append, reverse_transfer, mem_darts_reverse, reverse_copy, darts_reverse, SimpleGraph.Path.reverse_coe, reverse_bijective, isPath_reverse_iff, reverse_map, snd_reverse, IsCycle.reverse, IsTrail.reverse, length_reverse, nodup_tail_support_reverse, edges_reverse, reverse_singleton, reverse_isTrail_iff, support_reverse, reverse_cons, nil_reverse, IsPath.reverse, isCycle_reverse, reverseAux_eq_reverse_append, reverse_reverse, reverse_concat
reverseAux 📖CompOp
5 mathmath: length_reverseAux, cons_reverseAux, append_reverseAux, reverseAux_append, reverseAux_eq_reverse_append
tail 📖CompOp
18 mathmath: length_tail_add_one, tail_nil, IsHamiltonianCycle.isHamiltonian_tail, isHamiltonianCycle_isCycle_and_isHamiltonian_tail, getVert_tail, tail_cons_nil, tail_cons_eq, isCycle_iff_isPath_tail_and_le_length, Nil.tail, tail_cons, IsPath.disjoint_support_of_append, support_tail, support_tail_of_not_nil, IsPath.tail, cons_support_tail, IsSubwalk.tail, cons_tail_eq, IsCycle.isPath_tail
take 📖CompOp
15 mathmath: nil_take_iff, edges_take, darts_take, take_zero, append_take_drop_eq, take_of_length_le, take_length, isSubwalk_take, takeUntil_eq_take, take_add_heq, take_isSubwalk_take, take_cons_eq, take_getVert, take_add_eq, take_support_eq_support_take_succ

Theorems

NameKindAssumesProvesValidatesDepends On
append_assoc 📖mathematicalappendcons.congr_simp
append_concat 📖mathematicalSimpleGraph.Adjappend
concat
append_assoc
append_copy_copy 📖mathematicalappend
copy
append_nil 📖mathematicalappend
nil
cons.congr_simp
append_reverseAux 📖mathematicalreverseAux
append
SimpleGraph.symm
append_take_drop_eq 📖mathematicalappend
getVert
take
drop
ext_support
support_append
take_support_eq_support_take_succ
drop_support_eq_support_drop_min
min_eq_left_of_lt
length_support
coe_support_append 📖mathematicalMultiset.ofList
support
append
Multiset
Multiset.instAdd
Multiset.instSingleton
support_append
Multiset.coe_add
coe_support
coe_support_append' 📖mathematicalMultiset.ofList
support
append
Multiset
Multiset.instSub
Multiset.instAdd
Multiset.instSingleton
support_append
coe_support
add_comm
add_tsub_cancel_right
Multiset.instOrderedSub
Multiset.instAddLeftReflectLE
concatRec_concat 📖mathematicalSimpleGraph.AdjconcatRec
concat
reverse_reverse
rec_heq_of_heq
SimpleGraph.Adj.symm
SimpleGraph.symm
reverse_concat
concatRecAux.eq_2
concatRec_nil 📖mathematicalconcatRec
nil
concat_append 📖mathematicalSimpleGraph.Adjappend
concat
cons
concat_eq_append
append_assoc
cons_nil_append
concat_cons 📖mathematicalSimpleGraph.Adjconcat
cons
concat_dropLast 📖mathematicalSimpleGraph.Adj
penultimate
concat
dropLast
cons.congr_simp
concat_eq_append 📖mathematicalSimpleGraph.Adjconcat
append
cons
nil
concat_inj 📖mathematicalSimpleGraph.Adj
concat
copyconcat_ne_nil
concat_cons
concat_ne_nil 📖SimpleGraph.Adj
concat_nil 📖mathematicalSimpleGraph.Adjconcat
nil
cons
cons_append 📖mathematicalSimpleGraph.Adjappend
cons
cons_copy 📖mathematicalSimpleGraph.Adjcons
copy
cons_nil_append 📖mathematicalSimpleGraph.Adjappend
cons
nil
cons_reverseAux 📖mathematicalSimpleGraph.AdjreverseAux
cons
SimpleGraph.symm
cons_support_tail 📖mathematicalNilsupport
snd
tail
adj_snd
support_cons
cons_tail_eq
cons_tail_eq 📖mathematicalNilcons
snd
adj_snd
tail
adj_snd
getVert_zero
cons.congr_simp
tail_cons
cons_copy
copy_cons 📖mathematicalSimpleGraph.Adjcopy
cons
copy_copy 📖mathematicalcopy
copy_nil 📖mathematicalcopy
nil
copy_rfl_rfl 📖mathematicalcopy
dart_snd_mem_support_of_mem_darts 📖mathematicalSimpleGraph.Dart
darts
support
SimpleGraph.Dart.toProd
support_reverse
dart_fst_mem_support_of_mem_darts
darts_reverse
SimpleGraph.Dart.symm_symm
darts_append 📖mathematicaldarts
append
SimpleGraph.Dart
darts_concat 📖mathematicalSimpleGraph.Adjdarts
concat
SimpleGraph.Dart
darts_copy 📖mathematicaldarts
copy
darts_drop 📖mathematicaldarts
getVert
drop
SimpleGraph.Dart
getVert_zero
darts_reverse 📖mathematicaldarts
reverse
SimpleGraph.Dart
SimpleGraph.Dart.symm
SimpleGraph.symm
SimpleGraph.Adj.symm
reverse_cons
darts_append
darts_take 📖mathematicaldarts
getVert
take
SimpleGraph.Dart
dropLast_concat 📖mathematicalSimpleGraph.AdjdropLast
concat
copy
penultimate
penultimate_cons_of_not_nil
length_concat
dropLast_cons_of_not_nil
cons.congr_simp
copy.congr_simp
copy_copy
cons_copy
dropLast_cons_cons 📖mathematicalSimpleGraph.AdjdropLast
cons
penultimate
dropLast_cons_nil 📖mathematicalSimpleGraph.AdjdropLast
cons
nil
dropLast_cons_of_not_nil 📖mathematicalSimpleGraph.Adj
Nil
dropLast
cons
penultimate
copy
penultimate_cons_of_not_nil
penultimate_cons_of_not_nil
dropLast_nil 📖mathematicaldropLast
nil
drop_add_eq 📖mathematicaldrop
copy
getVert
drop_getVert
drop_getVert
drop_add_heq
drop_add_heq 📖mathematicalSimpleGraph.Walk
getVert
drop
add_comm
drop_cons_eq 📖mathematicalSimpleGraph.Adjdrop
cons
copy
getVert
getVert_cons
ext_support
getVert_cons
drop.eq_def
drop_getVert 📖mathematicalgetVert
drop
zero_add
add_right_comm
drop_length 📖mathematicallength
getVert
drop
drop_of_length_le 📖mathematicallengthdrop
copy
getVert
nil
getVert_of_length_le
Nil.eq_copy_nil
nil_drop_of_length_le
drop_support_eq_support_drop_min 📖mathematicalsupport
getVert
drop
length
min_self
inf_of_le_right
getVert_zero
inf_of_le_left
drop_zero 📖mathematicaldrop
copy
getVert
getVert_zero
getVert_zero
edgeSet_append 📖mathematicaledgeSet
append
Set
Sym2
Set.instUnion
Set.ext
edges_append
edgeSet_concat 📖mathematicalSimpleGraph.AdjedgeSet
concat
Sym2
Set
Set.instInsert
Set.ext
edges_concat
edgeSet_copy 📖mathematicaledgeSet
copy
Set.ext
edges_copy
edgeSet_reverse 📖mathematicaledgeSet
reverse
Set.ext
edges_reverse
edges_append 📖mathematicaledges
append
Sym2
darts_append
edges_concat 📖mathematicalSimpleGraph.Adjedges
concat
Sym2
darts_concat
edges_copy 📖mathematicaledges
copy
edges_drop 📖mathematicaledges
getVert
drop
Sym2
getVert_zero
edges_nodup_of_support_nodup 📖mathematicalsupportSym2
edges
fst_mem_support_of_mem_edges
edges_reverse 📖mathematicaledges
reverse
Sym2
darts_reverse
SimpleGraph.Dart.edge_comp_symm
edges_take 📖mathematicaledges
getVert
take
Sym2
exists_concat_eq_cons 📖mathematicalSimpleGraph.Adjconcat
cons
concat_cons
exists_cons_eq_concat 📖mathematicalSimpleGraph.Adjcons
concat
concat_cons
ext_getVert 📖getVertext_getVert_le_length
LE.le.antisymm
SimpleGraph.Adj.ne
adj_getVert_succ
getVert_of_length_le
le_of_not_ge
ext_getVert_le_length 📖length
getVert
le_or_gt
getVert_eq_support_getElem?
length_support
ext_support
ext_support 📖supportdarts_injective
Function.Injective.list_map
SimpleGraph.Dart.toProd_injective
Function.RightInverse.injective
List.rightInverse_unzip_zip
fst_mem_support_of_mem_edges 📖mathematicalSym2
edges
supportSimpleGraph.dart_edge_eq_mk'_iff'
dart_fst_mem_support_of_mem_darts
dart_snd_mem_support_of_mem_darts
getVert_append 📖mathematicalgetVert
append
length
getVert_zero
getVert_copy 📖mathematicalgetVert
copy
getVert_mem_tail_support 📖mathematicalNilsupport
getVert
getVert_tail
support_tail_of_not_nil
getVert_mem_support
getVert_reverse 📖mathematicalgetVert
reverse
length
SimpleGraph.symm
reverse_cons
getVert_append
length_reverse
LT.lt.le
eq_or_gt_of_not_lt
getVert_zero
zero_add
getVert_tail 📖mathematicalgetVert
snd
tail
getVert_zero
tail_cons
getVert_copy
length_append 📖mathematicallength
append
zero_add
add_comm
add_assoc
length_concat 📖mathematicalSimpleGraph.Adjlength
concat
length_append
length_copy 📖mathematicallength
copy
length_reverse 📖mathematicallength
reverse
length_reverseAux
add_zero
length_reverseAux 📖mathematicallength
reverseAux
zero_add
SimpleGraph.symm
add_assoc
length_tail_add_one 📖mathematicalNillength
snd
tail
adj_snd
length_cons
cons_tail_eq
mem_darts_reverse 📖mathematicalSimpleGraph.Dart
darts
reverse
SimpleGraph.Dart.symm
darts_reverse
mem_support_append_iff 📖mathematicalsupport
append
eq_or_ne
mem_support_of_mem_edges 📖mathematicalSym2
edges
SetLike.instMembership
Sym2.instSetLike
supportfst_mem_support_of_mem_edges
mem_tail_support_append_iff 📖mathematicalsupport
append
tail_support_append
nil_append 📖mathematicalappend
nil
nil_append_iff 📖mathematicalNil
append
append_nil
nil_copy 📖mathematicalNil
copy
nil_drop_iff 📖mathematicalNil
getVert
drop
length
nil_drop_of_length_le 📖mathematicallengthNil
getVert
drop
nil_iff_length_eq
drop_length
nil_reverse 📖mathematicalNil
reverse
SimpleGraph.symm
reverse_cons
nil_take_iff 📖mathematicalNil
getVert
take
nodup_tail_support_reverse 📖mathematicalsupport
reverse
List.nodup_tail_reverse
getVert_eq_support_getElem?
length_support
getVert_zero
getVert_length
support_reverse
not_nil_of_tail_not_nil 📖Nil
snd
tail
Nil.tail
penultimate_concat 📖mathematicalSimpleGraph.Adjpenultimate
concat
getVert_append
length_append
zero_add
getVert_zero
penultimate_reverse 📖mathematicalpenultimate
reverse
snd
SimpleGraph.symm
reverse_cons
getVert_append
length_append
length_reverse
zero_add
getVert_zero
reverseAux_append 📖mathematicalappend
reverseAux
SimpleGraph.symm
reverseAux_eq_reverse_append 📖mathematicalreverseAux
append
reverse
reverseAux_append
reverse_append 📖mathematicalreverse
append
append_reverseAux
reverseAux_append
reverse_bijective 📖mathematicalFunction.Bijective
SimpleGraph.Walk
reverse
reverse_injective
reverse_surjective
reverse_concat 📖mathematicalSimpleGraph.Adjreverse
concat
cons
SimpleGraph.symm
SimpleGraph.symm
reverse_append
reverse_cons
reverse_cons 📖mathematicalSimpleGraph.Adjreverse
cons
append
SimpleGraph.symm
nil
SimpleGraph.symm
reverseAux_append
reverse_copy 📖mathematicalreverse
copy
reverse_injective 📖mathematicalSimpleGraph.Walk
reverse
Function.RightInverse.injective
reverse_reverse
reverse_nil 📖mathematicalreverse
nil
reverse_reverse 📖mathematicalreverseSimpleGraph.symm
reverse_cons
reverse_append
reverse_singleton 📖mathematicalSimpleGraph.Adjreverse
cons
nil
SimpleGraph.symm
reverse_surjective 📖mathematicalSimpleGraph.Walk
reverse
reverse_reverse
reverse_toWalk 📖mathematicalSimpleGraph.Adjreverse
SimpleGraph.Adj.toWalk
SimpleGraph.Adj.symm
snd_mem_support_of_mem_edges 📖mathematicalSym2
edges
supportfst_mem_support_of_mem_edges
Sym2.eq_swap
snd_reverse 📖mathematicalsnd
reverse
penultimate
getVert_reverse
subset_support_append_left 📖mathematicalsupport
append
support_append
subset_support_append_right 📖mathematicalsupport
append
support_append 📖mathematicalsupport
append
append_nil
support_append_eq_support_dropLast_append 📖mathematicalsupport
append
support_concat 📖mathematicalSimpleGraph.Adjsupport
concat
support_copy 📖mathematicalsupport
copy
support_eq_concat 📖mathematicalsupportexists_cons_eq_concat
support_concat
support_injective 📖mathematicalSimpleGraph.Walk
support
ext_support
support_reverse 📖mathematicalsupport
reverse
SimpleGraph.symm
reverse_cons
support_append
support_subset_support_concat 📖mathematicalSimpleGraph.Adjsupport
concat
support_concat
support_tail 📖mathematicalNilsupport
snd
tail
support_tail_of_not_nil
support_tail_of_not_nil 📖mathematicalNilsupport
snd
tail
cons_support_tail
tail_cons 📖mathematicalSimpleGraph.Adjtail
cons
copy
getVert
getVert_zero
getVert_zero
tail_cons_eq 📖mathematicalSimpleGraph.Adjtail
cons
copy
getVert
getVert_zero
tail_cons
tail_cons_nil 📖mathematicalSimpleGraph.Adjtail
cons
nil
snd
tail_nil 📖mathematicaltail
nil
snd
tail_support_append 📖mathematicalsupport
append
support_append
support_ne_nil
take_add_eq 📖mathematicaltake
copy
getVert
drop
append
drop_getVert
drop_getVert
take_add_heq
take_add_heq 📖mathematicalSimpleGraph.Walk
getVert
take
drop
append
add_comm
append_nil
take_cons_eq 📖mathematicalSimpleGraph.Adjtake
cons
getVert
copy
getVert_cons
ext_support
getVert_cons
take_getVert 📖mathematicalgetVert
take
getVert_zero
min_self
inf_of_le_left
inf_of_le_right
take_length 📖mathematicallength
getVert
take
min_self
inf_of_le_right
inf_of_le_left
take_of_length_le 📖mathematicallengthtake
copy
getVert
getVert_of_length_le
getVert_of_length_le
length_cons
cons.congr_simp
cons_copy
take_support_eq_support_take_succ 📖mathematicalsupport
getVert
take
zero_add
take_zero 📖mathematicaltake
copy
getVert
nil
getVert_zero
getVert_zero

SimpleGraph.Walk.Nil

Theorems

NameKindAssumesProvesValidatesDepends On
append 📖mathematicalSimpleGraph.Walk.NilSimpleGraph.Walk.append
eq_copy_nil 📖mathematicalSimpleGraph.Walk.NilSimpleGraph.Walk.copy
SimpleGraph.Walk.nil
eq
eq
SimpleGraph.Walk.nil_iff_eq_nil
tail 📖mathematicalSimpleGraph.Walk.NilSimpleGraph.Walk.snd
SimpleGraph.Walk.tail

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