Mathlib Map

Theorems · Theorem · order theory

List.IsChain.sortedLT

∀ {α : Type u_1} {l : List α} [inst : Preorder α], List.IsChain (fun x1 x2 => x1 < x2) l → l.SortedLT

Alias of the reverse direction of List.sortedLT_iff_isChain.

Defined in
Mathlib.Data.List.Sort
Cited by
3 results in Mathlib
Foundations
Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Preorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CompositionSeries.toList_sorted · cited by 2CompositionSeries.toList_…SimplexCategoryGenRel.IsAdmissible.sortedLT · cited by 1IsAdmissible.sortedLTDenumerable.raise'_sorted · cited by 0Denumerable.raise'_sortedPreorder · cited by 7952PreorderList.SortedLT · cited by 66List.SortedLTList.sortedLT_iff_isChain · cited by 2List.sortedLT_iff_isChainIsChain.sortedLTCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.