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Theorems · Theorem · order theory

sup_iInf_eq

∀ {α : Type u} {ι : Sort w} [inst : Order.Coframe α] (a : α) (f : ι → α), a ⊔ ⨅ i, f i = ⨅ i, a ⊔ f i
Defined in
Mathlib.Order.CompleteBooleanAlgebra
Cited by
6 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Quot.sound
Assumes
Order.Coframe
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Around this declaration

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

Set.union_iInter · cited by 4Set.union_iInteriInf_sup_iInf · cited by 3iInf_sup_iInfMetric.infEDist_prod · cited by 2Metric.infEDist_prodsup_iInf₂_eq · cited by 1sup_iInf₂_eqsdiff_iInf_eq · cited by 1sdiff_iInf_eqSet.union_distrib_iInter_left · cited by 1Set.union_distrib_iInter_…iInf · cited by 1690iInfsup_comm · cited by 165sup_commOrder.Coframe · cited by 38Order.CoframeiInf_sup_eq · cited by 7iInf_sup_eqsup_iInf_eqCITED BYCITES

Cites4

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

Cited by6

Results whose statement or proof uses this declaration.