OrderEmbedding

(α : Type u_6) → (β : Type u_7) → [LE α] → [LE β] → Type (max u_6 u_7)

An order embedding is an embedding f : α ↪ β such that a ≤ b ↔ (f a) ≤ (f b). This definition is an abbreviation of RelEmbedding (≤) (≤).

Defined in: Mathlib.Order.Hom.Basic
Cited by: 619 results in Mathlib
Foundations: Depth 2 from the axioms, rests on 4 definitions · uses no axioms
Assumes: LE LE

Around this declaration

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

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

Results whose statement or proof uses this declaration.

Showing the 200 most cited of 762.