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Theorems · Theorem · order theory

iSup_disjoint_iff

∀ {α : Type u} {ι : Sort w} [inst : Order.Frame α] {a : α} {f : ι → α},
  Disjoint (⨆ i, f i) a ↔ ∀ (i : ι), Disjoint (f i) a
Defined in
Mathlib.Order.CompleteBooleanAlgebra
Cited by
2 results in Mathlib
Foundations
Depth 18 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.

disjoint_iSup_iff · cited by 3disjoint_iSup_iffSet.disjoint_iUnion_left · cited by 2Set.disjoint_iUnion_leftBot.bot · cited by 4720Bot.botiSup · cited by 2415iSupDisjoint · cited by 2201DisjointOrder.Frame · cited by 88Order.FrameiSup_inf_eq · cited by 7iSup_inf_eqiSup_disjoint_iffCITED BYCITES

Cites5

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

Cited by2

Results whose statement or proof uses this declaration.