Theorems · Theorem · order theory

Set.PartiallyWellOrderedOn.subsetProdLex

∀ {α : Type u_2} {β : Type u_3} [inst : PartialOrder α] [inst_1 : Preorder β] {s : Set (Lex (α × β))},
  ((fun x => (ofLex x).1) '' s).IsPWO → (∀ (a : α), {y | toLex (a, y) ∈ s}.IsPWO) → s.IsPWO

Defined in

Mathlib.Order.WellFoundedSet

Cited by

1 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderPreorder