Theorems · Theorem · order theory

InitialSeg.eq_or_principal

∀ {α : Type u_1} {β : Type u_2} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder β s] (f : InitialSeg r s),
  Function.Surjective ⇑f ∨ ∃ b, ∀ (x : β), x ∈ Set.range ⇑f ↔ s x b

An initial segment embedding is either an isomorphism, or a principal segment embedding. See also InitialSeg.ltOrEq.

Defined in

Mathlib.Order.InitialSeg

Cited by

0 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

IsWellOrder