Theorems · Definition · order theory

InitialSeg.antisymm

{α : Type u_1} →
  {β : Type u_2} →
    {r : α → α → Prop} → {s : β → β → Prop} → [IsWellOrder β s] → InitialSeg r s → InitialSeg s r → r ≃r s

If we have order embeddings between α and β whose ranges are initial segments, and β is a well order, then α and β are order-isomorphic.

Defined in

Mathlib.Order.InitialSeg

Cited by

2 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

IsWellOrder