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Theorems · Theorem · order theory

iInf_sup_eq

∀ {α : Type u} {ι : Sort w} [inst : Order.Coframe α] (f : ι → α) (a : α), (⨅ i, f i) ⊔ a = ⨅ i, f i ⊔ a
Defined in
Mathlib.Order.CompleteBooleanAlgebra
Cited by
7 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Quot.sound
Assumes
Order.Coframe
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

sup_iInf_eq · cited by 6sup_iInf_eqSet.iInter_union · cited by 4Set.iInter_unioniInf_sup_iInf · cited by 3iInf_sup_iInfMetric.infEDist_prod · cited by 2Metric.infEDist_prodiInf_codisjoint_iff · cited by 2iInf_codisjoint_iffSet.union_distrib_iInter_right · cited by 1Set.union_distrib_iInter_…iInf₂_sup_eq · cited by 1iInf₂_sup_eqiInf · cited by 1690iInfOrder.Coframe · cited by 38Order.CoframeiInf_range · cited by 27iInf_rangesInf_sup_eq · cited by 3sInf_sup_eqiInf_sup_eqCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by7

Results whose statement or proof uses this declaration.