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Theorems · Theorem · order theory

iSup_inf_eq

∀ {α : Type u} {ι : Sort w} [inst : Order.Frame 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.Frame
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Around this declaration

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

Set.iUnion_inter · cited by 27Set.iUnion_interinf_iSup_eq · cited by 4inf_iSup_eqiSup_inf_iSup · cited by 3iSup_inf_iSupAlgebraicGeometry.isIso_pushoutSection_of_iSup_eq · cited by 2AlgebraicGeometry.isIso_p…iSup_disjoint_iff · cited by 2iSup_disjoint_iffAlgebraicGeometry.isCompact_basicOpen · cited by 1AlgebraicGeometry.isCompa…iSup₂_inf_eq · cited by 0iSup₂_inf_eqiSup · cited by 2415iSupOrder.Frame · cited by 88Order.FrameiSup_range · cited by 24iSup_rangesSup_inf_eq · cited by 3sSup_inf_eqiSup_inf_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.