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Theorems · Theorem · order theory

Fin.antitone_iff_succ_le

∀ {n : ℕ} {α : Type u_1} [inst : Preorder α] {f : Fin (n + 1) → α}, Antitone f ↔ ∀ (i : Fin n), f i.succ ≤ f i.castSucc

A function f on Fin (n + 1) is antitone if and only if f (i + 1) ≤ f i for all i.

Defined in
Mathlib.Order.Fin.Basic
Cited by
0 results in Mathlib
Foundations
Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Preorder
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Preorder · cited by 7952PreorderAntitone · cited by 563Antitoneantitone_iff_forall_lt · cited by 7antitone_iff_forall_ltFin.liftFun_iff_succ · cited by 6Fin.liftFun_iff_succFin.antitone_iff_succ_leCITED BYCITES

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