Theorems · Theorem · order theory

upperBounds_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 → upperBounds (s ×ˢ t) = upperBounds s ×ˢ upperBounds t

Defined in: Mathlib.Order.Bounds.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 8 from the axioms · uses propext, Quot.sound
Assumes: Preorder Preorder

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement and proof · cited by 53,352
Preorderstatement and proof · cited by 7,952
Set.ofPredproof · cited by 6,101
Set.Nonemptystatement and proof · cited by 2,627
Set.extproof · cited by 2,266
SProd.sprodstatement · cited by 1,750
upperBoundsstatement · cited by 263
Set.nonempty_coe_sortproof · cited by 23

Cited by1

Results whose statement or proof uses this declaration.

IsLUB.prodproof · cited by 2