Theorems · Theorem · order theory

lowerBounds_prod

∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] {s : Set α} {t : Set β},
  s.Nonempty → t.Nonempty → lowerBounds (s ×ˢ t) = lowerBounds s ×ˢ lowerBounds t

Defined in

Mathlib.Order.Bounds.Basic

Cited by

1 results in Mathlib

Foundations

Depth 7 from the axioms · uses propext, Quot.sound

Assumes

PreorderPreorder