Theorems · Definition · order theory

InitialSeg.total

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

For any two well orders, one is an initial segment of the other.

Defined in

Mathlib.Order.InitialSeg

Cited by

0 results in Mathlib

Foundations

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

Assumes

IsWellOrderIsWellOrder