Documentation Verification Report

Chain

πŸ“ Source: Mathlib/Data/List/Chain.lean

Statistics

MetricCount
Definitionscons, cons_cons, chains, lex_chains
4
Theoremslist_chain', append, append_overlap, chain, cons', cons_of_le, cons_of_ne_nil, drop, getElem, iff, iff_mem, imp, induction, infix, init, iterate_eq_of_apply_eq, left_of_append, prefix, rel_head, rel_head?, right_of_append, sublist, suffix, tail, take, backwards_induction, backwards_induction_head, iff, iff_mem, induction, pairwise, rel, sublist, append, append_overlap, backwards_concat_induction, backwards_cons_induction, backwards_cons_induction_head, backwards_induction, concat_induction, concat_induction_head, cons, cons', cons_induction, cons_of_le, cons_of_ne_nil, drop, dropLast, iff, iff_mem, iff_mem_mem_tail, iff_of_mem_imp, iff_of_mem_tail_imp, imp_head, imp_of_mem_imp, imp_of_mem_tail_imp, induction, infix, isChain_cons, iterate_eq_of_apply_eq, left_of_append, prefix, rel_cons, rel_head, rel_head?, right_of_append, sublist, suffix, tail, take, chain', chain'_append, chain'_append_cons_cons, chain'_attach, chain'_attachWith, chain'_cons', chain'_cons_cons, chain'_eq_iff_eq_replicate, chain'_flatten, chain'_iff_forall_getElem, chain'_iff_forall_rel_of_append_cons_cons, chain'_iff_get, chain'_iff_pairwise, chain'_isInfix, chain'_map, chain'_map_of_chain', chain'_nil, chain'_of_chain'_map, chain'_of_not, chain'_pair, chain'_reverse, chain'_singleton, chain'_split, chain_append_cons_cons, chain_append_singleton_iff_forallβ‚‚, chain_eq_iff_eq_replicate, chain_iff, chain_iff_forallβ‚‚, chain_iff_get, chain_iff_pairwise, chain_map, chain_map_of_chain, chain_of_chain_map, chain_of_chain_pmap, chain_pmap_of_chain, chain_replicate_of_rel, chain_singleton, chain_split, exists_chain_of_relationReflTransGen, exists_isChain_cons_of_relationReflTransGen, exists_isChain_ne_nil_of_relationReflTransGen, exists_not_getElem_of_not_isChain, isChain_append, isChain_append_cons_cons, isChain_attach, isChain_attachWith, isChain_cons, isChain_cons', isChain_cons_append_cons_cons, isChain_cons_append_singleton_iff_forallβ‚‚, isChain_cons_eq_iff_eq_replicate, isChain_cons_iff, isChain_cons_iff_forallβ‚‚, isChain_cons_iff_get, isChain_cons_map, isChain_cons_map_of_isChain_cons, isChain_cons_of_isChain_cons_map, isChain_cons_of_isChain_cons_pmap, isChain_cons_pmap, isChain_cons_pmap_of_isChain_cons, isChain_cons_split, isChain_eq_iff_eq_replicate, isChain_flatten, isChain_iff, isChain_iff_forall_rel_of_append_cons_cons, isChain_iff_forallβ‚‚, isChain_iff_get, isChain_isInfix, isChain_map, isChain_map_of_isChain, isChain_nil, isChain_of_isChain_map, isChain_of_isChain_pmap, isChain_pair, isChain_pmap, isChain_pmap_of_isChain, isChain_replicate_of_rel, isChain_reverse, isChain_singleton, isChain_split, relationReflTransGen_of_exists_chain_cons, relationReflTransGen_of_exists_isChain, relationReflTransGen_of_exists_isChain_cons, list_chain', instIsWellFoundedChainsLex_chains
155
Total159

Acc

Theorems

NameKindAssumesProvesValidatesDepends On
list_chain' πŸ“–mathematicalβ€”List.chains
List.lex_chains
β€”List.isChain_cons

List

Definitions

NameCategoryTheorems
chains πŸ“–CompOp
3 mathmath: Acc.list_chain', WellFounded.list_chain', instIsWellFoundedChainsLex_chains
lex_chains πŸ“–MathDef
3 mathmath: Acc.list_chain', WellFounded.list_chain', instIsWellFoundedChainsLex_chains

Theorems

NameKindAssumesProvesValidatesDepends On
chain'_append πŸ“–β€”β€”β€”β€”isChain_append
chain'_append_cons_cons πŸ“–β€”β€”β€”β€”isChain_append_cons_cons
chain'_attach πŸ“–β€”β€”β€”β€”isChain_attach
chain'_attachWith πŸ“–β€”β€”β€”β€”isChain_attachWith
chain'_cons' πŸ“–β€”β€”β€”β€”isChain_cons
chain'_cons_cons πŸ“–β€”β€”β€”β€”β€”
chain'_eq_iff_eq_replicate πŸ“–β€”β€”β€”β€”isChain_eq_iff_eq_replicate
chain'_flatten πŸ“–β€”β€”β€”β€”isChain_flatten
chain'_iff_forall_getElem πŸ“–β€”β€”β€”β€”β€”
chain'_iff_forall_rel_of_append_cons_cons πŸ“–β€”β€”β€”β€”isChain_append_cons_cons
chain'_iff_get πŸ“–mathematicalβ€”LT.lt.ne'
Nat.instPreorder
β€”isChain_iff_get
chain'_iff_pairwise πŸ“–β€”β€”β€”β€”β€”
chain'_isInfix πŸ“–β€”β€”β€”β€”isChain_isInfix
chain'_map πŸ“–β€”β€”β€”β€”isChain_map
chain'_map_of_chain' πŸ“–β€”β€”β€”β€”isChain_map_of_isChain
chain'_nil πŸ“–β€”β€”β€”β€”isChain_nil
chain'_of_chain'_map πŸ“–β€”β€”β€”β€”isChain_of_isChain_map
chain'_of_not πŸ“–β€”β€”β€”β€”exists_not_getElem_of_not_isChain
chain'_pair πŸ“–β€”β€”β€”β€”isChain_pair
chain'_reverse πŸ“–β€”β€”β€”β€”isChain_reverse
chain'_singleton πŸ“–β€”β€”β€”β€”isChain_singleton
chain'_split πŸ“–β€”β€”β€”β€”isChain_split
chain_append_cons_cons πŸ“–β€”β€”β€”β€”isChain_cons_append_cons_cons
chain_append_singleton_iff_forallβ‚‚ πŸ“–β€”β€”β€”β€”isChain_cons_append_singleton_iff_forallβ‚‚
chain_eq_iff_eq_replicate πŸ“–β€”β€”β€”β€”isChain_cons_eq_iff_eq_replicate
chain_iff πŸ“–β€”β€”β€”β€”isChain_cons_iff
chain_iff_forallβ‚‚ πŸ“–β€”β€”β€”β€”isChain_cons_iff_forallβ‚‚
chain_iff_get πŸ“–β€”β€”β€”β€”isChain_cons_iff_get
chain_iff_pairwise πŸ“–β€”β€”β€”β€”β€”
chain_map πŸ“–β€”β€”β€”β€”isChain_cons_map
chain_map_of_chain πŸ“–β€”β€”β€”β€”isChain_cons_map_of_isChain_cons
chain_of_chain_map πŸ“–β€”β€”β€”β€”isChain_cons_of_isChain_cons_map
chain_of_chain_pmap πŸ“–β€”β€”β€”β€”isChain_cons_of_isChain_cons_pmap
chain_pmap_of_chain πŸ“–β€”β€”β€”β€”isChain_cons_pmap_of_isChain_cons
chain_replicate_of_rel πŸ“–β€”β€”β€”β€”isChain_replicate_of_rel
chain_singleton πŸ“–β€”β€”β€”β€”isChain_pair
chain_split πŸ“–β€”β€”β€”β€”isChain_cons_split
exists_chain_of_relationReflTransGen πŸ“–β€”Relation.ReflTransGenβ€”β€”exists_isChain_cons_of_relationReflTransGen
exists_isChain_cons_of_relationReflTransGen πŸ“–β€”Relation.ReflTransGenβ€”β€”Relation.ReflTransGen.head_induction_on
exists_isChain_ne_nil_of_relationReflTransGen πŸ“–β€”Relation.ReflTransGenβ€”β€”exists_isChain_cons_of_relationReflTransGen
exists_not_getElem_of_not_isChain πŸ“–β€”β€”β€”β€”β€”
isChain_append πŸ“–β€”β€”β€”β€”instIsEmptyFalse
isChain_append_cons_cons πŸ“–β€”β€”β€”β€”isChain_split
isChain_attach πŸ“–β€”β€”β€”β€”isChain_attachWith
isChain_attachWith πŸ“–β€”β€”β€”β€”β€”
isChain_cons πŸ“–β€”β€”β€”β€”IsChain.rel_head?
IsChain.tail
IsChain.cons
isChain_cons' πŸ“–β€”β€”β€”β€”isChain_cons
isChain_cons_append_cons_cons πŸ“–β€”β€”β€”β€”isChain_cons_split
isChain_cons_append_singleton_iff_forallβ‚‚ πŸ“–β€”β€”β€”β€”β€”
isChain_cons_eq_iff_eq_replicate πŸ“–β€”β€”β€”β€”β€”
isChain_cons_iff πŸ“–β€”β€”β€”β€”isChain_iff
isChain_cons_iff_forallβ‚‚ πŸ“–β€”β€”β€”β€”instIsEmptyFalse
isChain_cons_iff_get πŸ“–β€”β€”β€”β€”β€”
isChain_cons_map πŸ“–β€”β€”β€”β€”isChain_map
isChain_cons_map_of_isChain_cons πŸ“–β€”β€”β€”β€”isChain_cons_map
isChain_cons_of_isChain_cons_map πŸ“–β€”β€”β€”β€”isChain_cons_map
isChain_cons_of_isChain_cons_pmap πŸ“–β€”β€”β€”β€”isChain_cons_pmap
isChain_cons_pmap πŸ“–β€”β€”β€”β€”isChain_pmap
isChain_cons_pmap_of_isChain_cons πŸ“–β€”β€”β€”β€”isChain_cons_pmap
IsChain.imp_of_mem_imp
isChain_cons_split πŸ“–β€”β€”β€”β€”isChain_split
isChain_eq_iff_eq_replicate πŸ“–β€”β€”β€”β€”β€”
isChain_flatten πŸ“–β€”β€”β€”β€”instIsEmptyFalse
isChain_append
head?_append_of_ne_nil
Iff.and
isChain_iff πŸ“–β€”β€”β€”β€”β€”
isChain_iff_forall_rel_of_append_cons_cons πŸ“–β€”β€”β€”β€”isChain_append_cons_cons
isChain_iff_forallβ‚‚ πŸ“–β€”β€”β€”β€”instIsEmptyFalse
isChain_iff_get πŸ“–mathematicalβ€”LT.lt.ne'
Nat.instPreorder
β€”LT.lt.ne'
isChain_isInfix πŸ“–β€”β€”β€”β€”β€”
isChain_map πŸ“–β€”β€”β€”β€”β€”
isChain_map_of_isChain πŸ“–β€”β€”β€”β€”isChain_map
isChain_nil πŸ“–β€”β€”β€”β€”β€”
isChain_of_isChain_map πŸ“–β€”β€”β€”β€”isChain_map
isChain_of_isChain_pmap πŸ“–β€”β€”β€”β€”isChain_pmap
isChain_pair πŸ“–β€”β€”β€”β€”β€”
isChain_pmap πŸ“–β€”β€”β€”β€”β€”
isChain_pmap_of_isChain πŸ“–β€”β€”β€”β€”isChain_pmap
IsChain.imp_of_mem_imp
isChain_replicate_of_rel πŸ“–β€”β€”β€”β€”β€”
isChain_reverse πŸ“–β€”β€”β€”β€”isChain_split
isChain_pair
isChain_singleton πŸ“–β€”β€”β€”β€”β€”
isChain_split πŸ“–β€”β€”β€”β€”β€”
relationReflTransGen_of_exists_chain_cons πŸ“–mathematicalβ€”Relation.ReflTransGenβ€”relationReflTransGen_of_exists_isChain_cons
relationReflTransGen_of_exists_isChain πŸ“–mathematicalβ€”Relation.ReflTransGenβ€”IsChain.induction
relationReflTransGen_of_exists_isChain_cons πŸ“–mathematicalβ€”Relation.ReflTransGenβ€”IsChain.backwards_cons_induction_head
Relation.ReflTransGen.head

List.Chain

Theorems

NameKindAssumesProvesValidatesDepends On
backwards_induction πŸ“–β€”β€”β€”β€”List.IsChain.backwards_cons_induction
backwards_induction_head πŸ“–β€”β€”β€”β€”List.IsChain.backwards_cons_induction_head
iff πŸ“–β€”β€”β€”β€”List.IsChain.iff
iff_mem πŸ“–β€”β€”β€”β€”List.IsChain.iff_mem_mem_tail
induction πŸ“–β€”β€”β€”β€”List.IsChain.cons_induction
pairwise πŸ“–β€”β€”β€”β€”β€”
rel πŸ“–β€”β€”β€”β€”List.IsChain.rel_cons
sublist πŸ“–β€”β€”β€”β€”List.IsChain.sublist

List.Chain'

Definitions

NameCategoryTheorems
cons πŸ“–CompOpβ€”
cons_cons πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
append πŸ“–β€”β€”β€”β€”List.isChain_append
append_overlap πŸ“–β€”β€”β€”β€”List.IsChain.append_overlap
chain πŸ“–β€”β€”β€”β€”List.IsChain.isChain_cons
cons' πŸ“–β€”β€”β€”β€”List.IsChain.cons
cons_of_le πŸ“–β€”Preorder.toLT
PartialOrder.toPreorder
LinearOrder.toPartialOrder
List.LE'
β€”β€”List.IsChain.cons_of_le
cons_of_ne_nil πŸ“–β€”β€”β€”β€”List.IsChain.cons_of_ne_nil
drop πŸ“–β€”β€”β€”β€”List.IsChain.drop
getElem πŸ“–β€”β€”β€”β€”β€”
iff πŸ“–β€”β€”β€”β€”List.IsChain.iff
iff_mem πŸ“–β€”β€”β€”β€”List.IsChain.iff_mem
imp πŸ“–β€”β€”β€”β€”β€”
induction πŸ“–β€”β€”β€”β€”List.IsChain.induction
infix πŸ“–β€”β€”β€”β€”List.IsChain.infix
init πŸ“–β€”β€”β€”β€”List.IsChain.dropLast
iterate_eq_of_apply_eq πŸ“–mathematicalβ€”Nat.iterateβ€”List.IsChain.iterate_eq_of_apply_eq
left_of_append πŸ“–β€”β€”β€”β€”List.IsChain.left_of_append
prefix πŸ“–β€”β€”β€”β€”List.IsChain.prefix
rel_head πŸ“–β€”β€”β€”β€”List.IsChain.rel_head
rel_head? πŸ“–β€”β€”β€”β€”List.IsChain.rel_head?
right_of_append πŸ“–β€”β€”β€”β€”List.IsChain.right_of_append
sublist πŸ“–β€”β€”β€”β€”List.IsChain.sublist
suffix πŸ“–β€”β€”β€”β€”List.IsChain.suffix
tail πŸ“–β€”β€”β€”β€”List.IsChain.tail
take πŸ“–β€”β€”β€”β€”List.IsChain.take

List.IsChain

Theorems

NameKindAssumesProvesValidatesDepends On
append πŸ“–β€”β€”β€”β€”List.isChain_append
append_overlap πŸ“–β€”β€”β€”β€”append
right_of_append
List.getLast?_append_of_ne_nil
List.isChain_append
backwards_concat_induction πŸ“–β€”β€”β€”β€”backwards_induction
backwards_cons_induction πŸ“–β€”β€”β€”β€”backwards_induction
backwards_cons_induction_head πŸ“–β€”β€”β€”β€”backwards_cons_induction
backwards_induction πŸ“–β€”β€”β€”β€”induction
List.isChain_reverse
concat_induction πŸ“–β€”β€”β€”β€”induction
concat_induction_head πŸ“–β€”β€”β€”β€”concat_induction
cons πŸ“–β€”β€”β€”β€”β€”
cons' πŸ“–β€”β€”β€”β€”cons
cons_induction πŸ“–β€”β€”β€”β€”induction
cons_of_le πŸ“–β€”Preorder.toLT
PartialOrder.toPreorder
LinearOrder.toPartialOrder
List.LE'
β€”β€”lt_of_le_of_lt
le_iff_lt_or_eq
not_le
le_of_lt
List.lt_iff_lex_lt
cons_of_ne_nil πŸ“–β€”β€”β€”β€”β€”
drop πŸ“–β€”β€”β€”β€”suffix
dropLast πŸ“–β€”β€”β€”β€”prefix
iff πŸ“–β€”β€”β€”β€”β€”
iff_mem πŸ“–β€”β€”β€”β€”iff_of_mem_imp
iff_mem_mem_tail πŸ“–β€”β€”β€”β€”iff_of_mem_tail_imp
iff_of_mem_imp πŸ“–β€”β€”β€”β€”imp_of_mem_imp
iff_of_mem_tail_imp πŸ“–β€”β€”β€”β€”imp_of_mem_tail_imp
imp_head πŸ“–β€”β€”β€”β€”β€”
imp_of_mem_imp πŸ“–β€”β€”β€”β€”imp_of_mem_tail_imp
imp_of_mem_tail_imp πŸ“–β€”β€”β€”β€”β€”
induction πŸ“–β€”β€”β€”β€”β€”
infix πŸ“–β€”β€”β€”β€”right_of_append
left_of_append
isChain_cons πŸ“–β€”β€”β€”β€”β€”
iterate_eq_of_apply_eq πŸ“–mathematicalβ€”Nat.iterateβ€”Function.iterate_succ'
left_of_append πŸ“–β€”β€”β€”β€”List.isChain_append
prefix πŸ“–β€”β€”β€”β€”infix
rel_cons πŸ“–β€”β€”β€”β€”β€”
rel_head πŸ“–β€”β€”β€”β€”β€”
rel_head? πŸ“–β€”β€”β€”β€”rel_head
List.cons_head?_tail
right_of_append πŸ“–β€”β€”β€”β€”List.isChain_append
sublist πŸ“–β€”β€”β€”β€”β€”
suffix πŸ“–β€”β€”β€”β€”infix
tail πŸ“–β€”β€”β€”β€”β€”
take πŸ“–β€”β€”β€”β€”prefix

List.Pairwise

Theorems

NameKindAssumesProvesValidatesDepends On
chain' πŸ“–β€”β€”β€”β€”β€”

WellFounded

Theorems

NameKindAssumesProvesValidatesDepends On
list_chain' πŸ“–mathematicalβ€”List.chains
List.lex_chains
β€”Acc.list_chain'

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
instIsWellFoundedChainsLex_chains πŸ“–mathematicalβ€”IsWellFounded
List.chains
List.lex_chains
β€”WellFounded.list_chain'
IsWellFounded.wf

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