Documentation Verification Report

Sort

📁 Source: Mathlib/Data/List/Sort.lean

Statistics

MetricCount
DefinitionsSortedGE, SortedGT, SortedLE, SortedLT, decidableSortedGE, decidableSortedGT, decidableSortedLE, decidableSortedLT, insertionSort, orderedInsert
10
TheoremsofFn_sorted, sortedGE, sortedGE_ofFn, sortedGE, sortedGT, sortedLE, sortedLT, eq_of_mem_iff, insertionSort_eq, merge, orderedInsert, sortedGE, sortedGT, sortedLE, sortedLT, eq_of_pairwise', eq_of_sortedGE, eq_of_sortedLE, eq_reverse_of_sortedLE_of_sortedGE, eq_of_mem_iff, ge_of_gt, gt_of_ge, insertionSort_eq, le_of_lt, lt_of_le, merge, orderedInsert, antitone, antitone_get, getElem_ge_getElem_of_le, isChain, map_ofDual, map_toDual, of_map_ofDual, of_map_toDual, of_reverse, pairwise, reverse, sortedGT_of_nodup, eq_of_mem_iff, eq_reverse_of_mem_iff_of_sortedLT, getElem_gt_getElem_of_lt, getElem_le_getElem_iff, getElem_lt_getElem_iff, isChain, map_ofDual, map_toDual, nodup, of_map_ofDual, of_map_toDual, of_reverse, pairwise, reverse, sortedGE, strictAnti, strictAnti_get, getElem_le_getElem_of_le, isChain, map_ofDual, map_toDual, monotone, monotone_get, of_map_ofDual, of_map_toDual, of_reverse, pairwise, reverse, sortedLT_of_nodup, eq_of_mem_iff, eq_reverse_of_mem_iff_of_sortedGT, getElem_le_getElem_iff, getElem_lt_getElem_iff, getElem_lt_getElem_of_lt, isChain, map_ofDual, map_toDual, nodup, of_map_ofDual, of_map_toDual, of_reverse, pairwise, reverse, sortedLE, strictMono, strictMono_get, orderedInsert_sublist, antisymm_of_pairwise, antisymm_of_sortedGT, antisymm_of_sortedLT, cons_sublist_orderedInsert, eq_of_perm_of_sorted, erase_orderedInsert, erase_orderedInsert_of_notMem, insertionSort_cons, insertionSort_cons_eq_take_drop, insertionSort_cons_of_forall_rel, insertionSort_nil, length_insertionSort, map_insertionSort, map_orderedInsert, mem_insertionSort, mem_orderedInsert, mergeSort_eq_insertionSort, mergeSort_eq_self, orderedInsert_cons, orderedInsert_cons_of_le, orderedInsert_count, orderedInsert_eq_take_drop, orderedInsert_erase, orderedInsert_length, orderedInsert_nil, orderedInsert_of_le, orderedInsert_of_not_le, pair_sublist_insertionSort, pair_sublist_insertionSort', pairwise_insertionSort, pairwise_mergeSort', perm_insertionSort, perm_orderedInsert, sortedGE_iff_antitone_get, sortedGE_iff_getElem_ge_getElem_of_le, sortedGE_iff_isChain, sortedGE_iff_pairwise, sortedGE_insertionSort, sortedGE_map_ofDual, sortedGE_map_toDual, sortedGE_mergeSort, sortedGE_ofFn_iff, sortedGE_of_getElem_ge_getElem_of_le, sortedGE_reverse, sortedGT_iff_getElem_gt_getElem_of_lt, sortedGT_iff_isChain, sortedGT_iff_nodup_and_sortedGE, sortedGT_iff_pairwise, sortedGT_iff_strictAnti_get, sortedGT_map_ofDual, sortedGT_map_toDual, sortedGT_ofFn_iff, sortedGT_of_getElem_gt_getElem_of_lt, sortedGT_reverse, sortedLE_iff_getElem_le_getElem_of_le, sortedLE_iff_isChain, sortedLE_iff_monotone_get, sortedLE_iff_pairwise, sortedLE_insertionSort, sortedLE_map_ofDual, sortedLE_map_toDual, sortedLE_mergeSort, sortedLE_ofFn_iff, sortedLE_of_getElem_le_getElem_of_le, sortedLE_range', sortedLE_replicate, sortedLE_reverse, sortedLT_finRange, sortedLT_iff_getElem_lt_getElem_of_lt, sortedLT_iff_isChain, sortedLT_iff_nodup_and_sortedLE, sortedLT_iff_pairwise, sortedLT_iff_strictMono_get, sortedLT_map_ofDual, sortedLT_map_toDual, sortedLT_ofFn_iff, sortedLT_of_getElem_lt_getElem_of_lt, sortedLT_range, sortedLT_range', sortedLT_reverse, sorted_ge_ofFn_iff, sorted_gt_ofFn_iff, sorted_insertionSort, sorted_le_ofFn_iff, sorted_le_range, sorted_le_range', sorted_le_replicate, sorted_lt_ofFn_iff, sorted_lt_range, sorted_lt_range', sorted_mergeSort', sublist_insertionSort, sublist_insertionSort', sublist_of_subperm_of_pairwise, sublist_of_subperm_of_sorted, sublist_of_subperm_of_sortedGE, sublist_of_subperm_of_sortedLE, sublist_orderedInsert, ofFn_sorted, sortedLE, sortedLE_ofFn, sortedGE_listMap, sortedGT_listMap, sortedLE_listMap, sortedLT_listMap, sorted_ge_listMap, sorted_gt_listMap, sorted_le_listMap, sorted_lt_listMap, sortedGT_listMap, sortedLT_listMap, pairwise_listMap, pairwise_swap_listMap, sorted_listMap, sorted_swap_listMap, pairwise_listMap, pairwise_swap_listMap, sortedGE_listMap, sortedGT, sortedGT_listMap, sortedGT_ofFn, sortedLE_listMap, sortedLT_listMap, sortedGE_listMap, sortedGT_listMap, sortedLE_listMap, sortedLT, sortedLT_listMap, sortedLT_ofFn
215
Total225

Antitone

Theorems

NameKindAssumesProvesValidatesDepends On
ofFn_sorted 📖mathematicalAntitone
PartialOrder.toPreorder
Fin.instPartialOrder
List.SortedGEsortedGE_ofFn
sortedGE 📖mathematicalAntitone
PartialOrder.toPreorder
Fin.instPartialOrder
List.SortedGEList.sortedGE_iff_antitone_get
sortedGE_ofFn 📖mathematicalAntitone
PartialOrder.toPreorder
Fin.instPartialOrder
List.SortedGEList.sortedGE_ofFn_iff

List

Definitions

NameCategoryTheorems
SortedGE 📖MathDef
37 mathmath: OrderEmbedding.sorted_ge_listMap, sortedGE_iff_isChain, Antitone.ofFn_sorted, Pairwise.sortedGE, sortedGE_iff_pairwise, sortedGT_iff_nodup_and_sortedGE, Antitone.sortedGE_ofFn, StrictAnti.sortedLE_listMap, SortedLE.map_toDual, sortedGE_of_getElem_ge_getElem_of_le, sortedGE_iff_getElem_ge_getElem_of_le, sortedGE_map_ofDual, SortedGT.sortedGE, sortedLE_map_toDual, SortedLE.map_ofDual, StrictMono.sortedGE_listMap, Sorted.ge_of_gt, SortedLE.of_map_ofDual, OrderEmbedding.sortedGE_listMap, Antitone.sortedGE, YoungDiagram.equivListRowLens_apply_coe, SortedLE.of_map_toDual, sortedGE_map_toDual, sorted_ge_ofFn_iff, sortedLE_map_ofDual, sortedGE_iff_antitone_get, IsChain.sortedGE, sortedGE_mergeSort, YoungDiagram.equivListRowLens_symm_apply, sortedGE_reverse, sortedGE_insertionSort, sortedLE_reverse, YoungDiagram.rowLens_sorted, StrictAnti.sortedGE_listMap, SortedLE.of_reverse, sortedGE_ofFn_iff, SortedLE.reverse
SortedGT 📖MathDef
37 mathmath: SortedLT.of_reverse, sortedGT_map_ofDual, OrderIso.sortedGT_listMap, SortedLT.of_map_ofDual, sortedGT_iff_nodup_and_sortedGE, Finset.sortedGT_sort, Sorted.gt_of_ge, Ordinal.CNF.sorted, Pairwise.sortedGT, sortedGT_iff_pairwise, Ordinal.CNF_sorted, StrictAnti.sortedGT_listMap, sortedGT_iff_strictAnti_get, IsChain.sortedGT, SortedLT.reverse, sorted_gt_ofFn_iff, SortedLT.map_toDual, sortedLT_map_ofDual, SortedLT.of_map_toDual, sortedGT_ofFn_iff, Nat.sortedGT_map_snd_divisorsAntidiagonalList, Finset.sort_sorted_gt, sortedGT_map_toDual, sortedGT_of_getElem_gt_getElem_of_lt, sortedLT_map_toDual, StrictAnti.sortedGT_ofFn, sortedLT_reverse, StrictAnti.sortedLT_listMap, sortedGT_iff_getElem_gt_getElem_of_lt, SortedLT.map_ofDual, OrderEmbedding.sortedGT_listMap, StrictAnti.sortedGT, SortedGE.sortedGT_of_nodup, OrderEmbedding.sorted_gt_listMap, StrictMono.sortedGT_listMap, sortedGT_reverse, sortedGT_iff_isChain
SortedLE 📖MathDef
43 mathmath: Nat.primeFactorsList_sorted, sortedLE_mergeSort, sorted_le_replicate, Sorted.le_of_lt, SortedGE.reverse, sortedLE_of_getElem_le_getElem_of_le, sortedLE_iff_getElem_le_getElem_of_le, IsChain.sortedLE, StrictAnti.sortedLE_listMap, SortedGE.map_ofDual, sortedGE_map_ofDual, sortedLE_iff_pairwise, Monotone.sortedLE_ofFn, sortedLT_iff_nodup_and_sortedLE, SortedGE.of_reverse, sortedLE_insertionSort, exists_map_eq_of_sorted_nonempty_iff_wbtw, sortedLE_replicate, sortedLE_map_toDual, Monotone.ofFn_sorted, sorted_le_ofFn_iff, SortedGE.map_toDual, Monotone.sortedLE, sorted_le_range', exists_map_eq_of_sorted_iff_wbtw, SortedGE.of_map_ofDual, sortedLE_iff_isChain, Pairwise.sortedLE, sortedGE_map_toDual, OrderEmbedding.sortedLE_listMap, sortedLE_map_ofDual, OrderEmbedding.sorted_le_listMap, sortedLE_ofFn_iff, sortedLE_range', sortedGE_reverse, StrictMono.sortedLE_listMap, sortedLE_iff_monotone_get, sortedLE_reverse, sorted_le_range, StrictAnti.sortedGE_listMap, SortedGE.of_map_toDual, SortedLT.sortedLE, Denumerable.raise_sorted
SortedLT 📖MathDef
48 mathmath: sorted_lt_range, OrderEmbedding.sorted_lt_listMap, sortedGT_map_ofDual, Nat.sortedLT_map_fst_divisorsAntidiagonalList, sortedLT_iff_pairwise, Nat.bitIndices_sorted, Sorted.lt_of_le, OrderEmbedding.sortedLT_listMap, exists_map_eq_of_sorted_nonempty_iff_sbtw, StrictAnti.sortedGT_listMap, sortedLT_iff_nodup_and_sortedLE, sortedLT_of_getElem_lt_getElem_of_lt, StrictMono.sortedLT, SortedGT.of_map_ofDual, exists_map_eq_of_sorted_iff_sbtw, Denumerable.raise'_sorted, SortedGT.map_toDual, Finset.sort_sorted_lt, StrictMono.sortedLT_ofFn, sortedLT_map_ofDual, SimplexCategoryGenRel.IsAdmissible.sorted, sortedLT_iff_strictMono_get, SortedGT.map_ofDual, SortedGT.of_map_toDual, sortedLT_finRange, sortedLT_iff_getElem_lt_getElem_of_lt, Finset.sortedLT_sort, OrderIso.sortedLT_listMap, sortedLT_range', sortedGT_map_toDual, StrictMono.sortedLT_listMap, SimplexCategoryGenRel.IsAdmissible.pairwise, sorted_lt_ofFn_iff, SortedGT.of_reverse, sortedLT_map_toDual, CompositionSeries.toList_sorted, sortedLT_iff_isChain, Pairwise.sortedLT, sortedLT_reverse, StrictAnti.sortedLT_listMap, IsChain.sortedLT, SimplexCategoryGenRel.IsAdmissible.sortedLT, SortedLE.sortedLT_of_nodup, SortedGT.reverse, sorted_lt_range', sortedLT_ofFn_iff, sortedGT_reverse, sortedLT_range
decidableSortedGE 📖CompOp
decidableSortedGT 📖CompOp
decidableSortedLE 📖CompOp
decidableSortedLT 📖CompOp
insertionSort 📖CompOp
19 mathmath: length_insertionSort, pair_sublist_insertionSort', insertionSort_cons, sorted_insertionSort, insertionSort_cons_of_forall_rel, sortedLE_insertionSort, Pairwise.insertionSort_eq, sublist_insertionSort', pairwise_insertionSort, insertionSort_nil, Sorted.insertionSort_eq, map_insertionSort, pair_sublist_insertionSort, insertionSort_cons_eq_take_drop, sublist_insertionSort, sortedGE_insertionSort, mergeSort_eq_insertionSort, perm_insertionSort, mem_insertionSort
orderedInsert 📖CompOp
20 mathmath: perm_orderedInsert, orderedInsert_cons_of_le, orderedInsert_nil, orderedInsert_eq_take_drop, orderedInsert_cons, sublist_orderedInsert, Pairwise.orderedInsert, insertionSort_cons, erase_orderedInsert_of_notMem, Sublist.orderedInsert_sublist, cons_sublist_orderedInsert, orderedInsert_length, mem_orderedInsert, erase_orderedInsert, orderedInsert_erase, map_orderedInsert, orderedInsert_of_le, orderedInsert_count, Sorted.orderedInsert, orderedInsert_of_not_le

Theorems

NameKindAssumesProvesValidatesDepends On
cons_sublist_orderedInsert 📖mathematicalorderedInsert
eq_of_perm_of_sorted 📖
erase_orderedInsert 📖mathematicalorderedInsert
erase_orderedInsert_of_notMem 📖mathematicalorderedInsert
insertionSort_cons 📖mathematicalinsertionSort
orderedInsert
insertionSort_cons_eq_take_drop 📖mathematicalinsertionSortorderedInsert_eq_take_drop
insertionSort_cons_of_forall_rel 📖mathematicalinsertionSortinsertionSort_cons
orderedInsert_cons_of_le
mem_insertionSort
insertionSort_nil 📖mathematicalinsertionSort
length_insertionSort 📖mathematicalinsertionSortperm_insertionSort
map_insertionSort 📖mathematicalinsertionSortinsertionSort_nil
insertionSort_cons
map_orderedInsert
map_orderedInsert 📖mathematicalorderedInsert
mem_insertionSort 📖mathematicalinsertionSortperm_insertionSort
mem_orderedInsert 📖mathematicalorderedInsert
mergeSort_eq_insertionSort 📖mathematicalinsertionSortPerm.eq_of_pairwise'
pairwise_mergeSort'
pairwise_insertionSort
perm_insertionSort
mergeSort_eq_self 📖Perm.eq_of_pairwise'
pairwise_mergeSort'
orderedInsert_cons 📖mathematicalorderedInsert
orderedInsert_cons_of_le 📖mathematicalorderedInsert
orderedInsert_count 📖mathematicalorderedInsertperm_orderedInsert
orderedInsert_eq_take_drop 📖mathematicalorderedInsert
orderedInsert_erase 📖mathematicalorderedInsert
orderedInsert_length 📖mathematicalorderedInsert
orderedInsert_nil 📖mathematicalorderedInsert
orderedInsert_of_le 📖mathematicalorderedInsertorderedInsert_cons_of_le
orderedInsert_of_not_le 📖mathematicalorderedInsert
pair_sublist_insertionSort 📖mathematicalinsertionSortsublist_insertionSort
pair_sublist_insertionSort' 📖mathematicalinsertionSortsublist_insertionSort'
pairwise_insertionSort 📖mathematicalinsertionSortPairwise.orderedInsert
pairwise_mergeSort' 📖trans_of
total_of
perm_insertionSort 📖mathematicalinsertionSort
perm_orderedInsert 📖mathematicalorderedInsertorderedInsert_cons
sortedGE_iff_antitone_get 📖mathematicalSortedGE
Antitone
PartialOrder.toPreorder
Fin.instPartialOrder
sortedGE_iff_getElem_ge_getElem_of_le 📖mathematicalSortedGE
Preorder.toLE
SortedGE.antitone_get
Antitone.sortedGE
sortedGE_iff_isChain 📖mathematicalSortedGE
Preorder.toLE
sortedGE_iff_pairwise
sortedGE_iff_pairwise 📖mathematicalSortedGE
Preorder.toLE
sortedGE_insertionSort 📖mathematicalSortedGE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
insertionSort
Preorder.toLE
LinearOrder.toDecidableLE
Pairwise.sortedGE
pairwise_insertionSort
LE.total'
instIsTransGe
sortedGE_map_ofDual 📖mathematicalSortedGE
OrderDual
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
SortedLE
OrderDual.instPreorder
sortedGE_map_toDual 📖mathematicalSortedGE
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
SortedLE
sortedGE_mergeSort 📖mathematicalSortedGE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
LinearOrder.toDecidableLE
Pairwise.sortedGE
pairwise_mergeSort'
LE.total'
instIsTransGe
sortedGE_ofFn_iff 📖mathematicalSortedGE
Antitone
PartialOrder.toPreorder
Fin.instPartialOrder
get_ofFn
sortedGE_of_getElem_ge_getElem_of_le 📖mathematicalPreorder.toLESortedGEsortedGE_iff_getElem_ge_getElem_of_le
sortedGE_reverse 📖mathematicalSortedGE
SortedLE
sortedGT_iff_getElem_gt_getElem_of_lt 📖mathematicalSortedGT
Preorder.toLT
SortedGT.strictAnti_get
StrictAnti.sortedGT
sortedGT_iff_isChain 📖mathematicalSortedGT
Preorder.toLT
sortedGT_iff_pairwise
sortedGT_iff_nodup_and_sortedGE 📖mathematicalSortedGT
PartialOrder.toPreorder
SortedGE
SortedGT.nodup
SortedGT.sortedGE
SortedGE.sortedGT_of_nodup
sortedGT_iff_pairwise 📖mathematicalSortedGT
Preorder.toLT
sortedGT_iff_strictAnti_get 📖mathematicalSortedGT
StrictAnti
PartialOrder.toPreorder
Fin.instPartialOrder
sortedGT_map_ofDual 📖mathematicalSortedGT
OrderDual
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
SortedLT
OrderDual.instPreorder
sortedGT_map_toDual 📖mathematicalSortedGT
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
SortedLT
sortedGT_ofFn_iff 📖mathematicalSortedGT
StrictAnti
PartialOrder.toPreorder
Fin.instPartialOrder
get_ofFn
sortedGT_of_getElem_gt_getElem_of_lt 📖mathematicalPreorder.toLTSortedGTsortedGT_iff_getElem_gt_getElem_of_lt
sortedGT_reverse 📖mathematicalSortedGT
SortedLT
sortedLE_iff_getElem_le_getElem_of_le 📖mathematicalSortedLE
Preorder.toLE
SortedLE.monotone_get
Monotone.sortedLE
sortedLE_iff_isChain 📖mathematicalSortedLE
Preorder.toLE
sortedLE_iff_pairwise
sortedLE_iff_monotone_get 📖mathematicalSortedLE
Monotone
PartialOrder.toPreorder
Fin.instPartialOrder
sortedLE_iff_pairwise 📖mathematicalSortedLE
Preorder.toLE
sortedLE_insertionSort 📖mathematicalSortedLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
insertionSort
Preorder.toLE
LinearOrder.toDecidableLE
Pairwise.sortedLE
pairwise_insertionSort
LE.total
instIsTransLe
sortedLE_map_ofDual 📖mathematicalSortedLE
OrderDual
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
SortedGE
OrderDual.instPreorder
sortedLE_map_toDual 📖mathematicalSortedLE
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
SortedGE
sortedLE_mergeSort 📖mathematicalSortedLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
LinearOrder.toDecidableLE
Pairwise.sortedLE
pairwise_mergeSort'
LE.total
instIsTransLe
sortedLE_ofFn_iff 📖mathematicalSortedLE
Monotone
PartialOrder.toPreorder
Fin.instPartialOrder
get_ofFn
sortedLE_of_getElem_le_getElem_of_le 📖mathematicalPreorder.toLESortedLEsortedLE_iff_getElem_le_getElem_of_le
sortedLE_range' 📖mathematicalSortedLE
Nat.instPreorder
Pairwise.sortedLE
sortedLE_replicate 📖mathematicalSortedLEPairwise.sortedLE
le_rfl
sortedLE_reverse 📖mathematicalSortedLE
SortedGE
sortedLT_finRange 📖mathematicalSortedLT
PartialOrder.toPreorder
Fin.instPartialOrder
sortedLT_of_getElem_lt_getElem_of_lt
sortedLT_iff_getElem_lt_getElem_of_lt 📖mathematicalSortedLT
Preorder.toLT
SortedLT.strictMono_get
StrictMono.sortedLT
sortedLT_iff_isChain 📖mathematicalSortedLT
Preorder.toLT
sortedLT_iff_pairwise
sortedLT_iff_nodup_and_sortedLE 📖mathematicalSortedLT
PartialOrder.toPreorder
SortedLE
SortedLT.nodup
SortedLT.sortedLE
SortedLE.sortedLT_of_nodup
sortedLT_iff_pairwise 📖mathematicalSortedLT
Preorder.toLT
sortedLT_iff_strictMono_get 📖mathematicalSortedLT
StrictMono
PartialOrder.toPreorder
Fin.instPartialOrder
sortedLT_map_ofDual 📖mathematicalSortedLT
OrderDual
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
SortedGT
OrderDual.instPreorder
sortedLT_map_toDual 📖mathematicalSortedLT
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
SortedGT
sortedLT_ofFn_iff 📖mathematicalSortedLT
StrictMono
PartialOrder.toPreorder
Fin.instPartialOrder
get_ofFn
sortedLT_of_getElem_lt_getElem_of_lt 📖mathematicalPreorder.toLTSortedLTsortedLT_iff_getElem_lt_getElem_of_lt
sortedLT_range 📖mathematicalSortedLT
Nat.instPreorder
Pairwise.sortedLT
sortedLT_range' 📖mathematicalSortedLT
Nat.instPreorder
Pairwise.sortedLT
sortedLT_reverse 📖mathematicalSortedLT
SortedGT
sorted_ge_ofFn_iff 📖mathematicalSortedGE
Antitone
PartialOrder.toPreorder
Fin.instPartialOrder
sortedGE_ofFn_iff
sorted_gt_ofFn_iff 📖mathematicalSortedGT
StrictAnti
PartialOrder.toPreorder
Fin.instPartialOrder
sortedGT_ofFn_iff
sorted_insertionSort 📖mathematicalinsertionSortpairwise_insertionSort
sorted_le_ofFn_iff 📖mathematicalSortedLE
Monotone
PartialOrder.toPreorder
Fin.instPartialOrder
sortedLE_ofFn_iff
sorted_le_range 📖mathematicalSortedLE
Nat.instPreorder
SortedLT.sortedLE
sortedLT_range
sorted_le_range' 📖mathematicalSortedLE
Nat.instPreorder
SortedLT.sortedLE
sortedLT_range'
sorted_le_replicate 📖mathematicalSortedLEsortedLE_replicate
sorted_lt_ofFn_iff 📖mathematicalSortedLT
StrictMono
PartialOrder.toPreorder
Fin.instPartialOrder
sortedLT_ofFn_iff
sorted_lt_range 📖mathematicalSortedLT
Nat.instPreorder
sortedLT_range
sorted_lt_range' 📖mathematicalSortedLT
Nat.instPreorder
sortedLT_range'
sorted_mergeSort' 📖pairwise_mergeSort'
sublist_insertionSort 📖mathematicalinsertionSortsublist_orderedInsert
cons_sublist_orderedInsert
sublist_insertionSort' 📖mathematicalinsertionSortsublist_orderedInsert
orderedInsert_erase
Sublist.orderedInsert_sublist
pairwise_insertionSort
sublist_of_subperm_of_pairwise 📖Perm.eq_of_pairwise'
sublist_of_subperm_of_sorted 📖sublist_of_subperm_of_pairwise
sublist_of_subperm_of_sortedGE 📖SortedGE
PartialOrder.toPreorder
sublist_of_subperm_of_pairwise
instAntisymmGe
SortedGE.pairwise
sublist_of_subperm_of_sortedLE 📖SortedLE
PartialOrder.toPreorder
sublist_of_subperm_of_pairwise
instAntisymmLe
SortedLE.pairwise
sublist_orderedInsert 📖mathematicalorderedInsert

List.IsChain

Theorems

NameKindAssumesProvesValidatesDepends On
sortedGE 📖mathematicalPreorder.toLEList.SortedGEList.sortedGE_iff_isChain
sortedGT 📖mathematicalPreorder.toLTList.SortedGTList.sortedGT_iff_isChain
sortedLE 📖mathematicalPreorder.toLEList.SortedLEList.sortedLE_iff_isChain
sortedLT 📖mathematicalPreorder.toLTList.SortedLTList.sortedLT_iff_isChain

List.Pairwise

Theorems

NameKindAssumesProvesValidatesDepends On
eq_of_mem_iff 📖List.Subset.antisymm_of_pairwise
insertionSort_eq 📖mathematicalList.insertionSort
merge 📖trans
orderedInsert 📖mathematicalList.orderedInsertList.mem_orderedInsert
total_of
List.orderedInsert_cons
sortedGE 📖mathematicalPreorder.toLEList.SortedGEList.sortedGE_iff_pairwise
sortedGT 📖mathematicalPreorder.toLTList.SortedGTList.sortedGT_iff_pairwise
sortedLE 📖mathematicalPreorder.toLEList.SortedLEList.sortedLE_iff_pairwise
sortedLT 📖mathematicalPreorder.toLTList.SortedLTList.sortedLT_iff_pairwise

List.Perm

Theorems

NameKindAssumesProvesValidatesDepends On
eq_of_pairwise' 📖antisymm
eq_of_sortedGE 📖List.SortedGE
PartialOrder.toPreorder
eq_of_pairwise'
instAntisymmGe
List.SortedGE.pairwise
eq_of_sortedLE 📖List.SortedLE
PartialOrder.toPreorder
eq_of_pairwise'
instAntisymmLe
List.SortedLE.pairwise
eq_reverse_of_sortedLE_of_sortedGE 📖List.SortedLE
PartialOrder.toPreorder
List.SortedGE
eq_of_sortedLE
List.SortedGE.reverse
List.perm_reverse

List.Sorted

Theorems

NameKindAssumesProvesValidatesDepends On
eq_of_mem_iff 📖List.Pairwise.eq_of_mem_iff
ge_of_gt 📖mathematicalList.SortedGTList.SortedGEList.SortedGT.sortedGE
gt_of_ge 📖mathematicalList.SortedGE
PartialOrder.toPreorder
List.SortedGTList.SortedGE.sortedGT_of_nodup
insertionSort_eq 📖mathematicalList.insertionSortList.Pairwise.insertionSort_eq
le_of_lt 📖mathematicalList.SortedLTList.SortedLEList.SortedLT.sortedLE
lt_of_le 📖mathematicalList.SortedLE
PartialOrder.toPreorder
List.SortedLTList.SortedLE.sortedLT_of_nodup
merge 📖List.Pairwise.merge
orderedInsert 📖mathematicalList.orderedInsertList.Pairwise.orderedInsert

List.SortedGE

Theorems

NameKindAssumesProvesValidatesDepends On
antitone 📖mathematicalList.SortedGEAntitone
PartialOrder.toPreorder
Fin.instPartialOrder
List.sortedGE_ofFn_iff
antitone_get 📖mathematicalList.SortedGEAntitone
PartialOrder.toPreorder
Fin.instPartialOrder
List.sortedGE_iff_antitone_get
getElem_ge_getElem_of_le 📖mathematicalList.SortedGEPreorder.toLEList.sortedGE_iff_getElem_ge_getElem_of_le
isChain 📖mathematicalList.SortedGEPreorder.toLEList.sortedGE_iff_isChain
map_ofDual 📖mathematicalList.SortedGE
OrderDual
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
List.SortedLE
OrderDual.instPreorder
List.sortedGE_map_ofDual
map_toDual 📖mathematicalList.SortedGE
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
List.SortedLEList.sortedGE_map_toDual
of_map_ofDual 📖mathematicalList.SortedGE
OrderDual
OrderDual.instPreorder
List.SortedLE
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
List.sortedLE_map_ofDual
of_map_toDual 📖mathematicalList.SortedGEList.SortedLE
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
List.sortedLE_map_toDual
of_reverse 📖mathematicalList.SortedGEList.SortedLEList.sortedGE_reverse
pairwise 📖mathematicalList.SortedGEPreorder.toLEList.sortedGE_iff_pairwise
reverse 📖mathematicalList.SortedGEList.SortedLEList.sortedLE_reverse
sortedGT_of_nodup 📖mathematicalList.SortedGE
PartialOrder.toPreorder
List.SortedGTStrictAnti.sortedGT
Antitone.strictAnti_of_injective
antitone_get
List.Nodup.injective_get

List.SortedGT

Theorems

NameKindAssumesProvesValidatesDepends On
eq_of_mem_iff 📖List.SortedGT
PartialOrder.toPreorder
List.Pairwise.eq_of_mem_iff
instAntisymmGt
instIrreflGt
pairwise
eq_reverse_of_mem_iff_of_sortedLT 📖List.SortedGT
PartialOrder.toPreorder
List.SortedLT
eq_of_mem_iff
List.SortedLT.reverse
getElem_gt_getElem_of_lt 📖mathematicalList.SortedGTPreorder.toLTList.sortedGT_iff_getElem_gt_getElem_of_lt
getElem_le_getElem_iff 📖mathematicalList.SortedGT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLEStrictAnti.le_iff_ge
strictAnti_get
getElem_lt_getElem_iff 📖mathematicalList.SortedGT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLTStrictAnti.lt_iff_gt
strictAnti_get
isChain 📖mathematicalList.SortedGTPreorder.toLTList.sortedGT_iff_isChain
map_ofDual 📖mathematicalList.SortedGT
OrderDual
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
List.SortedLT
OrderDual.instPreorder
List.sortedGT_map_ofDual
map_toDual 📖mathematicalList.SortedGT
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
List.SortedLTList.sortedGT_map_toDual
nodup 📖List.SortedGTFunction.Injective.nodup
StrictAnti.injective
strictAnti_get
of_map_ofDual 📖mathematicalList.SortedGT
OrderDual
OrderDual.instPreorder
List.SortedLT
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
List.sortedLT_map_ofDual
of_map_toDual 📖mathematicalList.SortedGTList.SortedLT
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
List.sortedLT_map_toDual
of_reverse 📖mathematicalList.SortedGTList.SortedLTList.sortedGT_reverse
pairwise 📖mathematicalList.SortedGTPreorder.toLTList.sortedGT_iff_pairwise
reverse 📖mathematicalList.SortedGTList.SortedLTList.sortedLT_reverse
sortedGE 📖mathematicalList.SortedGTList.SortedGEAntitone.sortedGE
StrictAnti.antitone
strictAnti_get
strictAnti 📖mathematicalList.SortedGTStrictAnti
PartialOrder.toPreorder
Fin.instPartialOrder
List.sortedGT_ofFn_iff
strictAnti_get 📖mathematicalList.SortedGTStrictAnti
PartialOrder.toPreorder
Fin.instPartialOrder
List.sortedGT_iff_strictAnti_get

List.SortedLE

Theorems

NameKindAssumesProvesValidatesDepends On
getElem_le_getElem_of_le 📖mathematicalList.SortedLEPreorder.toLEList.sortedLE_iff_getElem_le_getElem_of_le
isChain 📖mathematicalList.SortedLEPreorder.toLEList.sortedLE_iff_isChain
map_ofDual 📖mathematicalList.SortedLE
OrderDual
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
List.SortedGE
OrderDual.instPreorder
List.sortedLE_map_ofDual
map_toDual 📖mathematicalList.SortedLE
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
List.SortedGEList.sortedLE_map_toDual
monotone 📖mathematicalList.SortedLEMonotone
PartialOrder.toPreorder
Fin.instPartialOrder
List.sortedLE_ofFn_iff
monotone_get 📖mathematicalList.SortedLEMonotone
PartialOrder.toPreorder
Fin.instPartialOrder
List.sortedLE_iff_monotone_get
of_map_ofDual 📖mathematicalList.SortedLE
OrderDual
OrderDual.instPreorder
List.SortedGE
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
List.sortedGE_map_ofDual
of_map_toDual 📖mathematicalList.SortedLEList.SortedGE
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
List.sortedGE_map_toDual
of_reverse 📖mathematicalList.SortedLEList.SortedGEList.sortedLE_reverse
pairwise 📖mathematicalList.SortedLEPreorder.toLEList.sortedLE_iff_pairwise
reverse 📖mathematicalList.SortedLEList.SortedGEList.sortedGE_reverse
sortedLT_of_nodup 📖mathematicalList.SortedLE
PartialOrder.toPreorder
List.SortedLTStrictMono.sortedLT
Monotone.strictMono_of_injective
monotone_get
List.Nodup.injective_get

List.SortedLT

Theorems

NameKindAssumesProvesValidatesDepends On
eq_of_mem_iff 📖List.SortedLT
PartialOrder.toPreorder
List.Pairwise.eq_of_mem_iff
instAntisymmLt
instIrreflLt
pairwise
eq_reverse_of_mem_iff_of_sortedGT 📖List.SortedLT
PartialOrder.toPreorder
List.SortedGT
eq_of_mem_iff
List.SortedGT.reverse
getElem_le_getElem_iff 📖mathematicalList.SortedLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLEStrictMono.le_iff_le
strictMono_get
getElem_lt_getElem_iff 📖mathematicalList.SortedLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLTStrictMono.lt_iff_lt
strictMono_get
getElem_lt_getElem_of_lt 📖mathematicalList.SortedLTPreorder.toLTList.sortedLT_iff_getElem_lt_getElem_of_lt
isChain 📖mathematicalList.SortedLTPreorder.toLTList.sortedLT_iff_isChain
map_ofDual 📖mathematicalList.SortedLT
OrderDual
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
List.SortedGT
OrderDual.instPreorder
List.sortedLT_map_ofDual
map_toDual 📖mathematicalList.SortedLT
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
List.SortedGTList.sortedLT_map_toDual
nodup 📖List.SortedLTFunction.Injective.nodup
StrictMono.injective
strictMono_get
of_map_ofDual 📖mathematicalList.SortedLT
OrderDual
OrderDual.instPreorder
List.SortedGT
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
List.sortedGT_map_ofDual
of_map_toDual 📖mathematicalList.SortedLT
OrderDual
OrderDual.instPreorder
List.SortedGT
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
List.sortedGT_map_toDual
of_reverse 📖mathematicalList.SortedLTList.SortedGTList.sortedLT_reverse
pairwise 📖mathematicalList.SortedLTPreorder.toLTList.sortedLT_iff_pairwise
reverse 📖mathematicalList.SortedLTList.SortedGTList.sortedGT_reverse
sortedLE 📖mathematicalList.SortedLTList.SortedLEMonotone.sortedLE
StrictMono.monotone
strictMono_get
strictMono 📖mathematicalList.SortedLTStrictMono
PartialOrder.toPreorder
Fin.instPartialOrder
List.sortedLT_ofFn_iff
strictMono_get 📖mathematicalList.SortedLTStrictMono
PartialOrder.toPreorder
Fin.instPartialOrder
List.sortedLT_iff_strictMono_get

List.Sublist

Theorems

NameKindAssumesProvesValidatesDepends On
orderedInsert_sublist 📖mathematicalList.orderedInsertList.orderedInsert_nil
List.orderedInsert_cons
trans_of

List.Subset

Theorems

NameKindAssumesProvesValidatesDepends On
antisymm_of_pairwise 📖List.Perm.eq_of_pairwise'
List.Pairwise.nodup
antisymm_of_sortedGT 📖List.SortedGT
PartialOrder.toPreorder
antisymm_of_pairwise
instAntisymmGt
instIrreflGt
List.SortedGT.pairwise
antisymm_of_sortedLT 📖List.SortedLT
PartialOrder.toPreorder
antisymm_of_pairwise
instAntisymmLt
instIrreflLt
List.SortedLT.pairwise

Monotone

Theorems

NameKindAssumesProvesValidatesDepends On
ofFn_sorted 📖mathematicalMonotone
PartialOrder.toPreorder
Fin.instPartialOrder
List.SortedLEsortedLE_ofFn
sortedLE 📖mathematicalMonotone
PartialOrder.toPreorder
Fin.instPartialOrder
List.SortedLEList.sortedLE_iff_monotone_get
sortedLE_ofFn 📖mathematicalMonotone
PartialOrder.toPreorder
Fin.instPartialOrder
List.SortedLEList.sortedLE_ofFn_iff

OrderEmbedding

Theorems

NameKindAssumesProvesValidatesDepends On
sortedGE_listMap 📖mathematicalList.SortedGE
DFunLike.coe
OrderEmbedding
Preorder.toLE
instFunLikeOrderEmbedding
sortedGT_listMap 📖mathematicalList.SortedGT
DFunLike.coe
OrderEmbedding
Preorder.toLE
instFunLikeOrderEmbedding
sortedLE_listMap 📖mathematicalList.SortedLE
DFunLike.coe
OrderEmbedding
Preorder.toLE
instFunLikeOrderEmbedding
RelEmbedding.pairwise_listMap
sortedLT_listMap 📖mathematicalList.SortedLT
DFunLike.coe
OrderEmbedding
Preorder.toLE
instFunLikeOrderEmbedding
RelEmbedding.pairwise_listMap
sorted_ge_listMap 📖mathematicalList.SortedGE
DFunLike.coe
OrderEmbedding
Preorder.toLE
instFunLikeOrderEmbedding
sortedGE_listMap
sorted_gt_listMap 📖mathematicalList.SortedGT
DFunLike.coe
OrderEmbedding
Preorder.toLE
instFunLikeOrderEmbedding
sortedGT_listMap
sorted_le_listMap 📖mathematicalList.SortedLE
DFunLike.coe
OrderEmbedding
Preorder.toLE
instFunLikeOrderEmbedding
sortedLE_listMap
sorted_lt_listMap 📖mathematicalList.SortedLT
DFunLike.coe
OrderEmbedding
Preorder.toLE
instFunLikeOrderEmbedding
sortedLT_listMap

OrderIso

Theorems

NameKindAssumesProvesValidatesDepends On
sortedGT_listMap 📖mathematicalList.SortedGT
DFunLike.coe
OrderIso
Preorder.toLE
instFunLikeOrderIso
OrderEmbedding.sortedGT_listMap
sortedLT_listMap 📖mathematicalList.SortedLT
DFunLike.coe
OrderIso
Preorder.toLE
instFunLikeOrderIso
OrderEmbedding.sortedLT_listMap

RelEmbedding

Theorems

NameKindAssumesProvesValidatesDepends On
pairwise_listMap 📖mathematicalDFunLike.coe
RelEmbedding
instFunLike
map_rel_iff
pairwise_swap_listMap 📖mathematicalFunction.swap
DFunLike.coe
RelEmbedding
instFunLike
map_rel_iff
sorted_listMap 📖mathematicalDFunLike.coe
RelEmbedding
instFunLike
pairwise_listMap
sorted_swap_listMap 📖mathematicalFunction.swap
DFunLike.coe
RelEmbedding
instFunLike
pairwise_swap_listMap

RelIso

Theorems

NameKindAssumesProvesValidatesDepends On
pairwise_listMap 📖mathematicalDFunLike.coe
RelIso
instFunLike
RelEmbedding.pairwise_listMap
pairwise_swap_listMap 📖mathematicalFunction.swap
DFunLike.coe
RelIso
instFunLike
RelEmbedding.pairwise_swap_listMap

StrictAnti

Theorems

NameKindAssumesProvesValidatesDepends On
sortedGE_listMap 📖mathematicalStrictAnti
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
List.SortedGE
List.SortedLE
StrictMono.sortedLE_listMap
dual_right
sortedGT 📖mathematicalStrictAnti
PartialOrder.toPreorder
Fin.instPartialOrder
List.SortedGTList.sortedGT_iff_strictAnti_get
sortedGT_listMap 📖mathematicalStrictAnti
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
List.SortedGT
List.SortedLT
StrictMono.sortedLT_listMap
dual_right
sortedGT_ofFn 📖mathematicalStrictAnti
PartialOrder.toPreorder
Fin.instPartialOrder
List.SortedGTList.sortedGT_ofFn_iff
sortedLE_listMap 📖mathematicalStrictAnti
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
List.SortedLE
List.SortedGE
StrictMono.sortedGE_listMap
dual_right
sortedLT_listMap 📖mathematicalStrictAnti
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
List.SortedLT
List.SortedGT
StrictMono.sortedGT_listMap
dual_right

StrictMono

Theorems

NameKindAssumesProvesValidatesDepends On
sortedGE_listMap 📖mathematicalStrictMono
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
List.SortedGEOrderEmbedding.sortedGE_listMap
sortedGT_listMap 📖mathematicalStrictMono
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
List.SortedGTOrderEmbedding.sortedGT_listMap
sortedLE_listMap 📖mathematicalStrictMono
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
List.SortedLEOrderEmbedding.sortedLE_listMap
sortedLT 📖mathematicalStrictMono
PartialOrder.toPreorder
Fin.instPartialOrder
List.SortedLTList.sortedLT_iff_strictMono_get
sortedLT_listMap 📖mathematicalStrictMono
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
List.SortedLTOrderEmbedding.sortedLT_listMap
sortedLT_ofFn 📖mathematicalStrictMono
PartialOrder.toPreorder
Fin.instPartialOrder
List.SortedLTList.sortedLT_ofFn_iff

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