Theorems · Theorem · order theory

InitialSeg.exists_sum_relIso

∀ {α : Type u_1} {r : α → α → Prop} {β : Type u} {s : β → β → Prop} [IsWellOrder β s] (f : InitialSeg r s),
  ∃ γ t, IsWellOrder γ t ∧ Nonempty (Sum.Lex r t ≃r s)

An initial segment can be extended to an isomorphism by joining a second well order to the domain.

Defined in

Mathlib.Order.InitialSeg

Cited by

0 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

IsWellOrder