Theorems · Theorem · order theory
iInf_sup_of_antitone
∀ {α : Type u} [inst : Order.Coframe α] {ι : Type u_1} [inst_1 : Preorder ι] [IsDirectedOrder ι] {f g : ι → α},
Antitone f → Antitone g → ⨅ i, f i ⊔ g i = (⨅ i, f i) ⊔ ⨅ i, g i- Defined in
- Mathlib.Order.CompleteBooleanAlgebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
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.
- Preorderstatement and proof · cited by 7,952
- iInfstatement · cited by 1,690
- Antitonestatement and proof · cited by 563
- IsDirectedOrderstatement and proof · cited by 316
- Order.Coframestatement and proof · cited by 38
- Antitone.dual_leftproof · cited by 33
- iInf_sup_of_monotoneproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Set.iInter_union_of_antitoneproof · cited by 1