Theorems · Theorem · order theory
iInf_sup_iInf
∀ {α : Type u} [inst : Order.Coframe α] {ι : Type u_1} {ι' : Type u_2} {f : ι → α} {g : ι' → α},
(⨅ i, f i) ⊔ ⨅ j, g j = ⨅ i, f i.1 ⊔ g i.2- Defined in
- Mathlib.Order.CompleteBooleanAlgebra
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- Order.Coframe
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.
- iInfstatement and proof · cited by 1,690
- Order.Coframestatement and proof · cited by 38
- iInf_prodproof · cited by 7
- iInf_sup_eqproof · cited by 7
- sup_iInf_eqproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- iInf_sup_of_monotoneproof · cited by 3
- biInf_sup_biInfproof · cited by 2
- SupClosed.countableInfClosureproof · cited by 0