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Theorems · Theorem · order theory

sSup_disjoint_iff

∀ {α : Type u} [inst : Order.Frame α] {a : α} {s : Set α}, Disjoint (sSup s) a ↔ ∀ b ∈ s, Disjoint b a
Defined in
Mathlib.Order.CompleteBooleanAlgebra
Cited by
2 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.disjoint_sUnion_left · cited by 4Set.disjoint_sUnion_leftdisjoint_sSup_iff · cited by 2disjoint_sSup_iffSet · cited by 53352SetBot.bot · cited by 4720Bot.botDisjoint · cited by 2201DisjointSupSet.sSup · cited by 954SupSet.sSupOrder.Frame · cited by 88Order.FramesSup_inf_eq · cited by 3sSup_inf_eqsSup_disjoint_iffCITED BYCITES

Cites6

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Cited by2

Results whose statement or proof uses this declaration.