Theorems · Theorem · order theory

Set.PartiallyWellOrderedOn.prod

∀ {α : Type u_2} {β : Type u_3} {r : α → α → Prop} {r' : β → β → Prop} {s : Set α} [IsPreorder α r] {t : Set β},
  s.PartiallyWellOrderedOn r →
    t.PartiallyWellOrderedOn r' → (s ×ˢ t).PartiallyWellOrderedOn fun x y => r x.1 y.1 ∧ r' x.2 y.2

Defined in

Mathlib.Order.WellFoundedSet

Cited by

1 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

IsPreorder