Theorems · Theorem · order theory
sInf_sup_sInf
∀ {α : Type u} [inst : Order.Coframe α] {s t : Set α}, sInf s ⊔ sInf t = ⨅ p ∈ s ×ˢ t, p.1 ⊔ p.2- Defined in
- Mathlib.Order.CompleteBooleanAlgebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- Order.Coframe
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- SProd.sprodstatement and proof · cited by 1,750
- iInfstatement and proof · cited by 1,690
- InfSet.sInfstatement · cited by 935
- Order.Coframestatement and proof · cited by 38
- sInf_eq_iInfproof · cited by 22
- biInf_sup_biInfproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Set.sInter_union_sInterproof · cited by 1