Theorems · Definition · order theory

RelEmbedding.ofMonotone

{α : Type u_1} →
  {β : Type u_2} →
    {r : α → α → Prop} →
      {s : β → β → Prop} →
        [Std.Trichotomous r] → [Std.Asymm s] → (f : α → β) → (∀ (a b : α), r a b → s (f a) (f b)) → r ↪r s

It suffices to prove f is monotone between strict relations to show it is a relation embedding.

Defined in

Mathlib.Order.RelIso.Basic

Cited by

5 results in Mathlib

Foundations

Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Std.TrichotomousStd.Asymm