Theorems · Theorem · order theory
List.SortedLT.pairwise
∀ {α : Type u_1} {l : List α} [inst : Preorder α], l.SortedLT → List.Pairwise (fun x1 x2 => x1 < x2) lAlias of the forward direction of List.sortedLT_iff_pairwise.
- Defined in
- Mathlib.Data.List.Sort
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- List.SortedLTstatement · cited by 66
- List.sortedLT_iff_pairwiseproof · cited by 3
Cited by9
Results whose statement or proof uses this declaration.
- CompositionSeries.extproof · cited by 3
- Nat.pairwise_divisorsAntidiagonalList_fstproof · cited by 3
- Nat.bitIndices_sortedproof · cited by 3
- List.SortedLT.eq_of_mem_iffproof · cited by 2
- Nat.pairwise_divisorsAntidiagonalList_sndproof · cited by 2
- List.exists_map_eq_of_sorted_nonempty_iff_sbtwproof · cited by 1
- List.Subset.antisymm_of_sortedLTproof · cited by 0
- SimplexCategoryGenRel.IsAdmissible.head_ltproof · cited by 0
- Nat.bitIndices_nodupproof · cited by 0