Theorems · Theorem · order theory
UpperSet.prod_eq_top
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] {s : UpperSet α} {t : UpperSet β},
s ×ˢ t = ⊤ ↔ s = ⊤ ∨ t = ⊤- Defined in
- Mathlib.Order.UpperLower.Prod
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- Preorderstatement and proof · cited by 7,952
- SProd.sprodstatement · cited by 1,750
- UpperSetstatement and proof · cited by 245
- Set.prod_eq_empty_iffproof · cited by 8
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