Theorems · Definition · order theory

PrincipalSeg.codRestrict

{α : Type u_1} →
  {β : Type u_2} →
    {r : α → α → Prop} →
      {s : β → β → Prop} →
        (p : Set β) →
          (f : PrincipalSeg r s) →
            (∀ (a : α), f.toRelEmbedding a ∈ p) → f.top ∈ p → PrincipalSeg r (Subrel s fun x => x ∈ p)

Restrict the codomain of a principal segment embedding.

Defined in

Mathlib.Order.InitialSeg

Cited by

2 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext, Quot.sound