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Theorems · Theorem · order theory

disjoint_sSup_iff

∀ {α : Type u} [inst : Order.Frame α] {a : α} {s : Set α}, Disjoint a (sSup s) ↔ ∀ b ∈ s, Disjoint a b
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.

Set.disjoint_sUnion_right · cited by 1Set.disjoint_sUnion_rightsSupIndep_iff_pairwiseDisjoint · cited by 1sSupIndep_iff_pairwiseDis…Set · cited by 53352SetDisjoint · cited by 2201DisjointSupSet.sSup · cited by 954SupSet.sSupOrder.Frame · cited by 88Order.FramesSup_disjoint_iff · cited by 2sSup_disjoint_iffdisjoint_sSup_iffCITED BYCITES

Cites5

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Cited by2

Results whose statement or proof uses this declaration.