Mathlib Map

Theorems · Theorem · order theory

List.sortedGT_ofFn_iff

∀ {α : Type u_1} [inst : Preorder α] {n : ℕ} {f : Fin n → α}, (List.ofFn f).SortedGT ↔ StrictAnti f

The list List.ofFn f is strictly sorted with respect to (· ≥ ·) if and only if f is strictly antitone.

Defined in
Mathlib.Data.List.Sort
Cited by
2 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Quot.sound
Assumes
Preorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

List.SortedGT.strictAnti · cited by 0SortedGT.strictAntiStrictAnti.sortedGT_ofFn · cited by 0StrictAnti.sortedGT_ofFnPreorder · cited by 7952PreorderStrictAnti · cited by 204StrictAntiList.SortedGT · cited by 54List.SortedGTList.get_ofFn · cited by 6List.get_ofFnList.sortedGT_ofFn_iffCITED BYCITES

Cites4

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

Cited by2

Results whose statement or proof uses this declaration.