Theorems · Theorem · order theory
LowerSet.prod_inf_prod
∀ {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) ×ˢ (t₁ ⊓ t₂)- Defined in
- Mathlib.Order.UpperLower.Prod
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- SProd.sprodstatement · cited by 1,750
- LowerSetstatement and proof · cited by 230
- LowerSet.extproof · cited by 29
- Set.prod_inter_prodproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- LowerSet.disjoint_prodproof · cited by 0