Theorems · Theorem · order theory
LowerSet.prod_le_prod_iff
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] {s₁ s₂ : LowerSet α} {t₁ t₂ : LowerSet β},
s₁ ×ˢ t₁ ≤ s₂ ×ˢ t₂ ↔ s₁ ≤ s₂ ∧ t₁ ≤ t₂ ∨ s₁ = ⊥ ∨ t₁ = ⊥- Defined in
- Mathlib.Order.UpperLower.Prod
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites5
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- Preorderstatement and proof · cited by 7,952
- Bot.botstatement and proof · cited by 4,720
- SProd.sprodstatement · cited by 1,750
- LowerSetstatement and proof · cited by 230
- Set.prod_subset_prod_iffproof · cited by 15
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