Theorems · Theorem · order theory

StrictMono.id_le

∀ {β : Type u_2} [inst : LinearOrder β] [WellFoundedLT β] {f : β → β}, StrictMono f → id ≤ f

A strictly monotone function f on a well-order satisfies x ≤ f x for all x.

Defined in

Mathlib.Order.WellFounded

Cited by

14 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderWellFoundedLT