Theorems · Definition · order theory

RelEmbedding.orderEmbeddingOfLTEmbedding

{α : Type u_2} →
  {β : Type u_3} →
    [inst : PartialOrder α] → [inst_1 : PartialOrder β] → ((fun x1 x2 => x1 < x2) ↪r fun x1 x2 => x1 < x2) → α ↪o β

Embeddings of partial orders that preserve < also preserve ≤.

Defined in

Mathlib.Order.Hom.Basic

Cited by

3 results in Mathlib

Foundations

Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderPartialOrder