Documentation Verification Report

Lemmas

📁 Source: Batteries/Data/List/Lemmas.lean

Statistics

MetricCount
Definitions0
Theoremsimp, imp', cons_of_imp, cons_of_imp_of_cons, cons_of_imp_of_imp, getElem, imp, of_cons, pairwise, rel, idxOf_getElem, chain, isChain, diff_right, erase_diff_erase_sublist, append_eq_of_isPrefixOf?_eq_some, append_eq_of_isSuffixOf?_eq_some, beq_iff_exists_findIdxNth, chain_cons, chain_lt_range', chain_of_chain_cons, chain_succ_range', cons_diff, cons_diff_of_mem, cons_diff_of_not_mem, cons_union, countBefore_cons, countBefore_cons_succ, countBefore_cons_succ_of_beq, countBefore_cons_succ_of_not_beq, countBefore_eq_count_take, countBefore_idxOfNth_of_lt_count, countBefore_le_count, countBefore_lt_count_getElem, countBefore_lt_count_of_lt_length_of_beq, countBefore_nil, countBefore_of_ge_length, countBefore_zero, countPBefore_cons, countPBefore_cons_succ, countPBefore_cons_succ_of_neg, countPBefore_cons_succ_of_pos, countPBefore_cons_zero, countPBefore_eq_countP_take, countPBefore_findIdxNth_of_lt_countP, countPBefore_le_countP, countPBefore_length, countPBefore_lt_countP_of_lt_length_of_pos, countPBefore_mono, countPBefore_nil, countPBefore_of_ge_length, countPBefore_succ, countPBefore_zero, count_getElem_take_lt_count, count_getElem_take_succ, diff_append, diff_cons, diff_cons_right, diff_eq_foldl, diff_erase, diff_nil, diff_sublist, diff_subset, disjoint_append_left, disjoint_append_right, disjoint_comm, disjoint_cons_left, disjoint_cons_right, disjoint_iff_ne, disjoint_left, disjoint_nil_left, disjoint_nil_right, disjoint_of_disjoint_append_left_left, disjoint_of_disjoint_append_left_right, disjoint_of_disjoint_append_right_left, disjoint_of_disjoint_append_right_right, disjoint_of_disjoint_cons_left, disjoint_of_disjoint_cons_right, disjoint_of_subset_left, disjoint_of_subset_right, disjoint_right, disjoint_singleton, disjoint_symm, disjoint_take_drop, dropInfix?_eq_some_iff, dropInfix?_go_eq_some_iff, dropInfix?_nil, dropLast_eq_eraseIdx, dropPrefix?_append_of_beq, dropPrefix?_eq_some_iff, dropPrefix?_nil, dropSuffix?_eq_some_iff, dropSuffix?_nil, eraseIdx_idxOf_eq_erase, erase_eq_self_iff_forall_bne, exists_of_replaceF, exists_or_eq_self_of_replaceF, extractP_eq_find?_eraseP, finRange_eq_nil_iff, finRange_eq_pmap_range, findIdxNth_cons, findIdxNth_cons_of_neg, findIdxNth_cons_of_pos, findIdxNth_cons_succ, findIdxNth_cons_succ_of_pos, findIdxNth_cons_zero, findIdxNth_cons_zero_of_pos, findIdxNth_countPBefore_of_lt_length_of_pos, findIdxNth_eq_findIdxNth_iff, findIdxNth_eq_findIdxNth_iff_of_left_lt_countP, findIdxNth_eq_findIdxNth_iff_of_right_lt_countP, findIdxNth_eq_findIdxNth_of_ge_countP_ge_countP, findIdxNth_eq_length_iff, findIdxNth_eq_length_of_ge_countP, findIdxNth_le_findIdxNth_iff, findIdxNth_le_length, findIdxNth_lt_findIdxNth_iff, findIdxNth_lt_findIdxNth_iff_of_lt_countP, findIdxNth_lt_length_iff, findIdxNth_lt_length_of_lt_countP, findIdxNth_mono, findIdxNth_nil, findIdxNth_zero, findIdx_add_mem_findIdxs, findIdx_eq_findIdx?, findIdx_mem_findIdxs, findIdxsValues_eq_zip_filter_findIdxs, findIdxs_append, findIdxs_cons, findIdxs_eq_filterMap_zipIdx, findIdxs_eq_nil_iff, findIdxs_map, findIdxs_nil, findIdxs_singleton, findIdxs_start, findIdxs_take, foldlIdx_cons, foldlIdx_const, foldlIdx_eq_foldl_zipIdx, foldlIdx_nil, foldlIdx_start, foldrIdx_cons, foldrIdx_const, foldrIdx_eq_foldr_zipIdx, foldrIdx_nil, foldrIdx_start, foldr_eq_foldl, forIn_eq_bindList, ge_of_mem_findIdxs, ge_of_mem_idxsOf, get?_set_of_lt, get?_set_of_lt', getElem?_set_eq_of_lt, getElem?_set_of_lt, getElem?_set_of_lt', getElem_filter_eq_getElem_getElem_findIdxs, getElem_filter_eq_getElem_getElem_findIdxs_sub, getElem_findIdxs_eq_findIdxNth, getElem_findIdxs_eq_findIdxNth_add, getElem_findIdxs_lt, getElem_getElem_findIdxs, getElem_getElem_findIdxs_sub, getElem_getElem_idxsOf, getElem_getElem_idxsOf_of_lawful, getElem_getElem_idxsOf_sub, getElem_getElem_idxsOf_sub_of_lawful, getElem_idxOf, getElem_idxOfNth_beq, getElem_idxOfNth_eq, getElem_idxOf_eq_idxOfNth, getElem_idxOf_eq_idxOfNth_add, getElem_idxsOf_lt, getElem_mk, getElem_zero_findIdxs_eq_findIdx, getElem_zero_findIdxs_eq_findIdx_add, getElem_zero_idxsOf_eq_idxOf, getElem_zero_idxsOf_eq_idxOf_add, get_finRange, idxOfNth_cons, idxOfNth_cons_of_beq, idxOfNth_cons_of_not_beq, idxOfNth_cons_succ, idxOfNth_cons_succ_of_beq, idxOfNth_cons_zero, idxOfNth_cons_zero_of_beq, idxOfNth_countBefore_getElem, idxOfNth_countBefore_of_lt_length_of_beq, idxOfNth_eq_idxOfNth_iff, idxOfNth_eq_idxOfNth_iff_of_left_lt_count, idxOfNth_eq_idxOfNth_iff_of_right_lt_count, idxOfNth_eq_idxOfNth_of_ge_countP_ge_countP, idxOfNth_eq_length_iff, idxOfNth_eq_length_of_ge_count, idxOfNth_le_length, idxOfNth_lt_idxOfNth_iff, idxOfNth_lt_idxOfNth_iff_of_lt_count, idxOfNth_lt_length_iff, idxOfNth_lt_length_of_lt_count, idxOfNth_mono, idxOfNth_nil, idxOfNth_zero, idxOf_add_mem_idxsOf, idxOf_eq_getD_idxOf?, idxOf_eq_idxOf?, idxOf_mem_idxsOf, idxsOf_append, idxsOf_cons, idxsOf_eq_filterMap_zipIdx, idxsOf_eq_nil_iff, idxsOf_map, idxsOf_nil, idxsOf_start, idxsOf_take, insertP_cons_neg, insertP_cons_pos, insertP_loop, insertP_nil, instNeZeroNatLengthCons, inter_def, isChain_cons_of_isChain_cons_cons, isChain_findIdxs, isChain_idxsOf, isChain_iff_getElem, isChain_iff_pairwise, isChain_lt_range', isChain_of_isChain_cons, isChain_of_isChain_cons_cons, isChain_range', isPrefixOf?_eq_some_iff_append_eq, isSome_isPrefixOf?_eq_isPrefixOf, isSome_isSuffixOf?_eq_isSuffixOf, isSuffixOf?_eq_some_iff_append_eq, le_getElem_findIdxs, le_getElem_idxsOf, length_findIdxs, length_idxsOf, length_insertP, length_replaceF, length_tail_add_one, lt_add_of_mem_findIdxs, lt_add_of_mem_idxsOf, map_coe_finRange_eq_range, map_getElem_finRange, map_get_finRange, mem_diff_of_mem, mem_findIdxs_iff_exists_getElem_pos, mem_findIdxs_iff_getElem_sub_pos, mem_findIdxs_iff_pos_getElem, mem_idxsOf_getElem, mem_idxsOf_iff_exists_getElem_pos, mem_idxsOf_iff_getElem_pos, mem_idxsOf_iff_getElem_sub_pos, mem_insertP, mem_inter_iff, mem_union_iff, modify_eq_set_get, modify_eq_set_get?, modify_eq_set_getElem?, next?_cons, next?_nil, nil_diff, nil_union, nodup_finRange, nodup_findIdxs, nodup_idxsOf, pair_mem_product, pairwise_cons_cons, pairwise_findIdxs, pairwise_idxsOf, pairwise_le_finRange, pairwise_lt_finRange, pos_findIdxNth_getElem, pos_iff_exists_findIdxNth, prod_append, prod_concat, prod_cons, prod_eq_foldl, prod_eq_foldr, prod_flatten, prod_nil, prod_one_cons, prod_pair, prod_singleton, rel_of_chain_cons, rel_of_isChain_cons_cons, replaceF_cons, replaceF_cons_of_none, replaceF_cons_of_some, replaceF_nil, replaceF_of_forall_none, reverse_singleton, set_eq_modify, set_eq_take_cons_drop, singleton_disjoint, sum_append, sum_concat, sum_eq_foldl, sum_eq_foldr, sum_flatten, sum_pair, sum_singleton, sum_zero_cons, take_succ_drop, union_def, unzip_findIdxsValues
305
Total305

List

Theorems

NameKindAssumesProvesValidatesDepends On
append_eq_of_isPrefixOf?_eq_some 📖
append_eq_of_isSuffixOf?_eq_some 📖
beq_iff_exists_findIdxNth 📖mathematicalidxOfNth
chain_cons 📖mathematicalIsChainisChain_cons_cons
chain_lt_range' 📖mathematicalIsChainisChain_lt_range'
chain_of_chain_cons 📖IsChainisChain_cons_of_isChain_cons_cons
chain_succ_range' 📖mathematicalIsChainisChain_range'
cons_diff 📖mathematicaldiffdiff_cons
cons_diff_of_mem 📖mathematicaldiffcons_diff
cons_diff_of_not_mem 📖mathematicaldiffcons_diff
cons_union 📖mathematicalinstUnionOfBEq_batteries
countBefore_cons 📖mathematicalcountBeforecountPBefore_cons
countBefore_cons_succ 📖mathematicalcountBefore
countBefore_cons_succ_of_beq 📖mathematicalcountBefore
countBefore_cons_succ_of_not_beq 📖mathematicalcountBefore
countBefore_eq_count_take 📖mathematicalcountBefore
countBefore_idxOfNth_of_lt_count 📖mathematicalcountBefore
idxOfNth
countPBefore_findIdxNth_of_lt_countP
countBefore_le_count 📖mathematicalcountBefore
countBefore_lt_count_getElem 📖mathematicalcountBeforecountBefore_lt_count_of_lt_length_of_beq
countBefore_lt_count_of_lt_length_of_beq 📖mathematicalcountBeforecountPBefore_lt_countP_of_lt_length_of_pos
countBefore_nil 📖mathematicalcountBefore
countBefore_of_ge_length 📖mathematicalcountBeforecountPBefore_of_ge_length
countBefore_zero 📖mathematicalcountBeforecountPBefore_zero
countPBefore_cons 📖mathematicalcountPBefore
countPBefore_cons_succ 📖mathematicalcountPBefore
countPBefore_cons_succ_of_neg 📖mathematicalcountPBefore
countPBefore_cons_succ_of_pos 📖mathematicalcountPBefore
countPBefore_cons_zero 📖mathematicalcountPBefore
countPBefore_eq_countP_take 📖mathematicalcountPBefore
countPBefore_findIdxNth_of_lt_countP 📖mathematicalcountPBefore
findIdxNth
countPBefore_le_countP 📖mathematicalcountPBeforecountPBefore_eq_countP_take
countPBefore_length 📖mathematicalcountPBeforecountPBefore_of_ge_length
countPBefore_lt_countP_of_lt_length_of_pos 📖mathematicalcountPBeforefindIdxNth_lt_length_iff
findIdxNth_countPBefore_of_lt_length_of_pos
countPBefore_mono 📖mathematicalcountPBeforecountPBefore_eq_countP_take
countPBefore_nil 📖mathematicalcountPBefore
countPBefore_of_ge_length 📖mathematicalcountPBeforecountPBefore_eq_countP_take
countPBefore_succ 📖mathematicalcountPBefore
countPBefore_zero 📖mathematicalcountPBefore
count_getElem_take_lt_count 📖count_getElem_take_succ
count_getElem_take_succ 📖
diff_append 📖mathematicaldiffdiff_eq_foldl
diff_cons 📖mathematicaldiff
diff_cons_right 📖mathematicaldiffdiff_cons
diff_eq_foldl 📖mathematicaldiffdiff_cons
diff_erase 📖mathematicaldiffdiff_cons_right
diff_cons
diff_nil 📖mathematicaldiff
diff_sublist 📖mathematicaldiffdiff_cons
diff_subset 📖mathematicaldiffdiff_sublist
disjoint_append_left 📖mathematicalDisjoint
disjoint_append_right 📖mathematicalDisjointdisjoint_comm
disjoint_append_left
disjoint_comm 📖mathematicalDisjointdisjoint_symm
disjoint_cons_left 📖mathematicalDisjointdisjoint_append_left
disjoint_cons_right 📖mathematicalDisjointdisjoint_comm
disjoint_cons_left
disjoint_iff_ne 📖mathematicalDisjoint
disjoint_left 📖mathematicalDisjoint
disjoint_nil_left 📖mathematicalDisjoint
disjoint_nil_right 📖mathematicalDisjointdisjoint_comm
disjoint_nil_left
disjoint_of_disjoint_append_left_left 📖Disjointdisjoint_append_left
disjoint_of_disjoint_append_left_right 📖Disjointdisjoint_append_left
disjoint_of_disjoint_append_right_left 📖Disjointdisjoint_append_right
disjoint_of_disjoint_append_right_right 📖Disjointdisjoint_append_right
disjoint_of_disjoint_cons_left 📖Disjointdisjoint_of_subset_left
disjoint_of_disjoint_cons_right 📖Disjointdisjoint_of_subset_right
disjoint_of_subset_left 📖Disjoint
disjoint_of_subset_right 📖Disjoint
disjoint_right 📖mathematicalDisjointdisjoint_comm
disjoint_singleton 📖mathematicalDisjointdisjoint_comm
singleton_disjoint
disjoint_symm 📖Disjoint
disjoint_take_drop 📖mathematicalDisjoint
dropInfix?_eq_some_iff 📖mathematicaldropInfix?dropInfix?_go_eq_some_iff
dropInfix?_go_eq_some_iff 📖mathematicaldropInfix?.go
dropInfix?_nil 📖mathematicaldropInfix?
dropLast_eq_eraseIdx 📖
dropPrefix?_append_of_beq 📖mathematicaldropPrefix?
dropPrefix?_eq_some_iff 📖mathematicaldropPrefix?
dropPrefix?_nil 📖mathematicaldropPrefix?dropPrefix?.eq_1
dropSuffix?_eq_some_iff 📖mathematicaldropSuffix?
dropSuffix?_nil 📖mathematicaldropSuffix?
eraseIdx_idxOf_eq_erase 📖
erase_eq_self_iff_forall_bne 📖
exists_of_replaceF 📖mathematicalreplaceF
exists_or_eq_self_of_replaceF 📖mathematicalreplaceFexists_of_replaceF
replaceF_of_forall_none
extractP_eq_find?_eraseP 📖mathematicalextractPextractP.go.induct_unfolding
finRange_eq_nil_iff 📖
finRange_eq_pmap_range 📖
findIdxNth_cons 📖mathematicalfindIdxNth
findIdxNth_cons_of_neg 📖mathematicalfindIdxNth
findIdxNth_cons_of_pos 📖mathematicalfindIdxNth
findIdxNth_cons_succ 📖mathematicalfindIdxNth
findIdxNth_cons_succ_of_pos 📖mathematicalfindIdxNth
findIdxNth_cons_zero 📖mathematicalfindIdxNth
findIdxNth_cons_zero_of_pos 📖mathematicalfindIdxNth
findIdxNth_countPBefore_of_lt_length_of_pos 📖mathematicalfindIdxNth
countPBefore
findIdxNth_eq_findIdxNth_iff 📖mathematicalfindIdxNth
findIdxNth_eq_findIdxNth_iff_of_left_lt_countP 📖mathematicalfindIdxNth
findIdxNth_eq_findIdxNth_iff_of_right_lt_countP 📖mathematicalfindIdxNth
findIdxNth_eq_findIdxNth_of_ge_countP_ge_countP 📖mathematicalfindIdxNth
findIdxNth_eq_length_iff 📖mathematicalfindIdxNth
findIdxNth_eq_length_of_ge_countP 📖mathematicalfindIdxNth
findIdxNth_le_findIdxNth_iff 📖mathematicalfindIdxNthfindIdxNth_cons_zero
findIdxNth_cons_succ
findIdxNth_le_length 📖mathematicalfindIdxNth
findIdxNth_lt_findIdxNth_iff 📖mathematicalfindIdxNth
findIdxNth_lt_findIdxNth_iff_of_lt_countP 📖mathematicalfindIdxNth
findIdxNth_lt_length_iff 📖mathematicalfindIdxNth
findIdxNth_lt_length_of_lt_countP 📖mathematicalfindIdxNth
findIdxNth_mono 📖mathematicalfindIdxNth
findIdxNth_nil 📖mathematicalfindIdxNth
findIdxNth_zero 📖mathematicalfindIdxNth
findIdx_add_mem_findIdxs 📖mathematicalfindIdxs
findIdx_eq_findIdx? 📖
findIdx_mem_findIdxs 📖mathematicalfindIdxsfindIdx_add_mem_findIdxs
findIdxsValues_eq_zip_filter_findIdxs 📖mathematicalfindIdxsValues
findIdxs
findIdxs_append 📖mathematicalfindIdxs
findIdxs_cons 📖mathematicalfindIdxs
findIdxs_eq_filterMap_zipIdx 📖mathematicalfindIdxs
findIdxs_eq_nil_iff 📖mathematicalfindIdxs
findIdxs_map 📖mathematicalfindIdxs
findIdxs_nil 📖mathematicalfindIdxs
findIdxs_singleton 📖mathematicalfindIdxs
findIdxs_start 📖mathematicalfindIdxs
findIdxs_take 📖mathematicalfindIdxs
foldlIdx_cons 📖mathematicalfoldlIdx
foldlIdx_const 📖mathematicalfoldlIdx
foldlIdx_eq_foldl_zipIdx 📖mathematicalfoldlIdx
foldlIdx_nil 📖mathematicalfoldlIdx
foldlIdx_start 📖mathematicalfoldlIdx
foldrIdx_cons 📖mathematicalfoldrIdx
foldrIdx_const 📖mathematicalfoldrIdx
foldrIdx_eq_foldr_zipIdx 📖mathematicalfoldrIdx
foldrIdx_nil 📖mathematicalfoldrIdx
foldrIdx_start 📖mathematicalfoldrIdx
foldr_eq_foldl 📖
forIn_eq_bindList 📖mathematicalForInStep.run
ForInStep.bindList
ForInStep.done_bindList
ge_of_mem_findIdxs 📖findIdxs
ge_of_mem_idxsOf 📖idxsOf
get?_set_of_lt 📖getElem?_set_of_lt
get?_set_of_lt' 📖getElem?_set_of_lt'
getElem?_set_eq_of_lt 📖
getElem?_set_of_lt 📖
getElem?_set_of_lt' 📖
getElem_filter_eq_getElem_getElem_findIdxs 📖mathematicalfindIdxsgetElem_filter_eq_getElem_getElem_findIdxs_sub
getElem_filter_eq_getElem_getElem_findIdxs_sub 📖mathematicalfindIdxs
getElem_findIdxs_eq_findIdxNth 📖mathematicalfindIdxsfindIdxNthgetElem_findIdxs_eq_findIdxNth_add
getElem_findIdxs_eq_findIdxNth_add 📖mathematicalfindIdxsfindIdxNth
getElem_findIdxs_lt 📖findIdxs
getElem_getElem_findIdxs 📖findIdxsgetElem_getElem_findIdxs_sub
getElem_getElem_findIdxs_sub 📖findIdxsgetElem_filter_eq_getElem_getElem_findIdxs_sub
getElem_getElem_idxsOf 📖idxsOf
getElem_getElem_idxsOf_of_lawful 📖idxsOf
getElem_getElem_idxsOf_sub 📖idxsOfgetElem_getElem_findIdxs_sub
getElem_getElem_idxsOf_sub_of_lawful 📖idxsOf
getElem_idxOf 📖
getElem_idxOfNth_beq 📖idxOfNthpos_findIdxNth_getElem
getElem_idxOfNth_eq 📖idxOfNthgetElem_idxOfNth_beq
getElem_idxOf_eq_idxOfNth 📖mathematicalidxsOfidxOfNthgetElem_idxOf_eq_idxOfNth_add
getElem_idxOf_eq_idxOfNth_add 📖mathematicalidxsOfidxOfNth
getElem_idxsOf_lt 📖idxsOf
getElem_mk 📖
getElem_zero_findIdxs_eq_findIdx 📖findIdxsgetElem_zero_findIdxs_eq_findIdx_add
getElem_zero_findIdxs_eq_findIdx_add 📖findIdxs
getElem_zero_idxsOf_eq_idxOf 📖idxsOfgetElem_zero_idxsOf_eq_idxOf_add
getElem_zero_idxsOf_eq_idxOf_add 📖idxsOfgetElem_zero_findIdxs_eq_findIdx_add
get_finRange 📖
idxOfNth_cons 📖mathematicalidxOfNthfindIdxNth_cons
idxOfNth_cons_of_beq 📖mathematicalidxOfNth
idxOfNth_cons_of_not_beq 📖mathematicalidxOfNth
idxOfNth_cons_succ 📖mathematicalidxOfNth
idxOfNth_cons_succ_of_beq 📖mathematicalidxOfNth
idxOfNth_cons_zero 📖mathematicalidxOfNth
idxOfNth_cons_zero_of_beq 📖mathematicalidxOfNth
idxOfNth_countBefore_getElem 📖mathematicalidxOfNth
countBefore
idxOfNth_countBefore_of_lt_length_of_beq
idxOfNth_countBefore_of_lt_length_of_beq 📖mathematicalidxOfNth
countBefore
findIdxNth_countPBefore_of_lt_length_of_pos
idxOfNth_eq_idxOfNth_iff 📖mathematicalidxOfNthfindIdxNth_eq_findIdxNth_iff
idxOfNth_eq_idxOfNth_iff_of_left_lt_count 📖mathematicalidxOfNthfindIdxNth_eq_findIdxNth_iff_of_left_lt_countP
idxOfNth_eq_idxOfNth_iff_of_right_lt_count 📖mathematicalidxOfNthfindIdxNth_eq_findIdxNth_iff_of_right_lt_countP
idxOfNth_eq_idxOfNth_of_ge_countP_ge_countP 📖mathematicalidxOfNthfindIdxNth_eq_findIdxNth_of_ge_countP_ge_countP
idxOfNth_eq_length_iff 📖mathematicalidxOfNthfindIdxNth_eq_length_iff
idxOfNth_eq_length_of_ge_count 📖mathematicalidxOfNth
idxOfNth_le_length 📖mathematicalidxOfNthfindIdxNth_le_length
idxOfNth_lt_idxOfNth_iff 📖mathematicalidxOfNthfindIdxNth_lt_findIdxNth_iff
idxOfNth_lt_idxOfNth_iff_of_lt_count 📖mathematicalidxOfNthfindIdxNth_lt_findIdxNth_iff_of_lt_countP
idxOfNth_lt_length_iff 📖mathematicalidxOfNthfindIdxNth_lt_length_iff
idxOfNth_lt_length_of_lt_count 📖mathematicalidxOfNth
idxOfNth_mono 📖mathematicalidxOfNthfindIdxNth_mono
idxOfNth_nil 📖mathematicalidxOfNth
idxOfNth_zero 📖mathematicalidxOfNth
idxOf_add_mem_idxsOf 📖mathematicalidxsOffindIdx_add_mem_findIdxs
idxOf_eq_getD_idxOf? 📖
idxOf_eq_idxOf? 📖idxOf_eq_getD_idxOf?
idxOf_mem_idxsOf 📖mathematicalidxsOfidxOf_add_mem_idxsOf
idxsOf_append 📖mathematicalidxsOffindIdxs_append
idxsOf_cons 📖mathematicalidxsOffindIdxs_cons
idxsOf_eq_filterMap_zipIdx 📖mathematicalidxsOffindIdxs_eq_filterMap_zipIdx
idxsOf_eq_nil_iff 📖mathematicalidxsOffindIdxs_eq_nil_iff
idxsOf_map 📖mathematicalidxsOf
findIdxs
findIdxs_map
idxsOf_nil 📖mathematicalidxsOf
idxsOf_start 📖mathematicalidxsOffindIdxs_start
idxsOf_take 📖mathematicalidxsOffindIdxs_take
insertP_cons_neg 📖mathematicalinsertPinsertP_loop
insertP_cons_pos 📖mathematicalinsertP
insertP_loop 📖mathematicalinsertP.loop
insertP
insertP_nil 📖mathematicalinsertP
instNeZeroNatLengthCons 📖
inter_def 📖mathematicalinstInterOfBEq_batteries
isChain_cons_of_isChain_cons_cons 📖IsChainIsChain.of_cons
isChain_findIdxs 📖mathematicalIsChain
findIdxs
Pairwise.isChain
pairwise_findIdxs
isChain_idxsOf 📖mathematicalIsChain
idxsOf
Pairwise.isChain
pairwise_idxsOf
isChain_iff_getElem 📖mathematicalIsChain
isChain_iff_pairwise 📖mathematicalIsChain
isChain_lt_range' 📖mathematicalIsChainIsChain.imp
isChain_range'
isChain_of_isChain_cons 📖IsChain
isChain_of_isChain_cons_cons 📖IsChainIsChain.of_cons
isChain_range' 📖mathematicalIsChain
isPrefixOf?_eq_some_iff_append_eq 📖
isSome_isPrefixOf?_eq_isPrefixOf 📖
isSome_isSuffixOf?_eq_isSuffixOf 📖isSome_isPrefixOf?_eq_isPrefixOf
isSuffixOf?_eq_some_iff_append_eq 📖
le_getElem_findIdxs 📖findIdxs
le_getElem_idxsOf 📖idxsOf
length_findIdxs 📖mathematicalfindIdxs
length_idxsOf 📖mathematicalidxsOflength_findIdxs
length_insertP 📖mathematicalinsertPinsertP_loop
length_replaceF 📖mathematicalreplaceF
length_tail_add_one 📖
lt_add_of_mem_findIdxs 📖findIdxs
lt_add_of_mem_idxsOf 📖idxsOf
map_coe_finRange_eq_range 📖
map_getElem_finRange 📖
map_get_finRange 📖
mem_diff_of_mem 📖mathematicaldiffdiff_cons
mem_findIdxs_iff_exists_getElem_pos 📖mathematicalfindIdxs
mem_findIdxs_iff_getElem_sub_pos 📖mathematicalfindIdxs
mem_findIdxs_iff_pos_getElem 📖mathematicalfindIdxs
mem_idxsOf_getElem 📖mathematicalidxsOf
mem_idxsOf_iff_exists_getElem_pos 📖mathematicalidxsOf
mem_idxsOf_iff_getElem_pos 📖mathematicalidxsOf
mem_idxsOf_iff_getElem_sub_pos 📖mathematicalidxsOfmem_findIdxs_iff_getElem_sub_pos
mem_insertP 📖mathematicalinsertPinsertP_loop
mem_inter_iff 📖mathematicalinstInterOfBEq_batteries
mem_union_iff 📖mathematicalinstUnionOfBEq_batteriesnil_union
cons_union
modify_eq_set_get 📖modify_eq_set_getElem?
modify_eq_set_get? 📖modify_eq_set_getElem?
modify_eq_set_getElem? 📖
next?_cons 📖mathematicalnext?
next?_nil 📖mathematicalnext?
nil_diff 📖mathematicaldiffdiff_cons
nil_union 📖mathematicalinstUnionOfBEq_batteries
nodup_finRange 📖finRange_eq_pmap_range
nodup_findIdxs 📖mathematicalfindIdxspairwise_findIdxs
nodup_idxsOf 📖mathematicalidxsOfpairwise_idxsOf
pair_mem_product 📖mathematicalproduct
pairwise_cons_cons 📖
pairwise_findIdxs 📖mathematicalfindIdxs
pairwise_idxsOf 📖mathematicalidxsOfpairwise_findIdxs
pairwise_le_finRange 📖finRange_eq_pmap_range
pairwise_lt_finRange 📖finRange_eq_pmap_range
pos_findIdxNth_getElem 📖findIdxNth
pos_iff_exists_findIdxNth 📖mathematicalfindIdxNth
prod_append 📖mathematicalprod
prod_concat 📖mathematicalprodprod_append
prod_cons 📖mathematicalprod
prod_eq_foldl 📖mathematicalprodfoldr_eq_foldl
prod_eq_foldr 📖mathematicalprod
prod_flatten 📖mathematicalprodprod_append
prod_nil 📖mathematicalprod
prod_one_cons 📖mathematicalprod
prod_pair 📖mathematicalprod
prod_singleton 📖mathematicalprod
rel_of_chain_cons 📖IsChainrel_of_isChain_cons_cons
rel_of_isChain_cons_cons 📖IsChainisChain_cons_cons
replaceF_cons 📖mathematicalreplaceF
replaceF_cons_of_none 📖mathematicalreplaceF
replaceF_cons_of_some 📖mathematicalreplaceF
replaceF_nil 📖mathematicalreplaceF
replaceF_of_forall_none 📖mathematicalreplaceF
reverse_singleton 📖
set_eq_modify 📖
set_eq_take_cons_drop 📖set_eq_modify
singleton_disjoint 📖mathematicalDisjoint
sum_append 📖
sum_concat 📖sum_append
sum_eq_foldl 📖foldr_eq_foldl
sum_eq_foldr 📖
sum_flatten 📖sum_append
sum_pair 📖
sum_singleton 📖
sum_zero_cons 📖
take_succ_drop 📖
union_def 📖mathematicalinstUnionOfBEq_batteries
unzip_findIdxsValues 📖mathematicalfindIdxsValues
findIdxs

List.Chain

Theorems

NameKindAssumesProvesValidatesDepends On
imp 📖List.IsChainList.IsChain.imp
imp' 📖List.IsChainList.IsChain.cons_of_imp_of_imp

List.IsChain

Theorems

NameKindAssumesProvesValidatesDepends On
cons_of_imp 📖List.IsChain
cons_of_imp_of_cons 📖List.IsChaincons_of_imp
cons_of_imp_of_imp 📖List.IsChain
getElem 📖List.IsChainList.isChain_iff_getElem
imp 📖List.IsChain
of_cons 📖List.IsChainList.isChain_of_isChain_cons
pairwise 📖List.IsChainList.isChain_iff_pairwise
rel 📖List.IsChainList.rel_of_isChain_cons_cons

List.Nodup

Theorems

NameKindAssumesProvesValidatesDepends On
idxOf_getElem 📖

List.Pairwise

Theorems

NameKindAssumesProvesValidatesDepends On
chain 📖mathematicalList.IsChainisChain
isChain 📖mathematicalList.IsChain

List.Sublist

Theorems

NameKindAssumesProvesValidatesDepends On
diff_right 📖mathematicalList.diffList.diff_cons
erase_diff_erase_sublist 📖mathematicalList.diffList.diff_cons

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