Theorems · Definition · order theory

RelEmbedding.collapse

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

Construct an initial segment embedding r ≼i s by "filling in the gaps". That is, each subsequent element in α is mapped to the least element in β that hasn't been used yet. This construction is guaranteed to work as long as there exists some relation embedding r ↪r s.

Defined in

Mathlib.Order.InitialSeg

Cited by

2 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

IsWellOrder