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Theorems · Theorem · order theory

compl_eq_sSup_disjoint

∀ {α : Type u} [inst : Order.Frame α] {a : α}, aᶜ = sSup {w | Disjoint w a}
Defined in
Mathlib.Order.CompleteBooleanAlgebra
Cited by
1 results in Mathlib
Foundations
Depth 12 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.

TopologicalSpace.Opens.mem_compl · cited by 0Opens.mem_complSet.ofPred · cited by 6101Set.ofPredCompl.compl · cited by 2925Compl.complDisjoint · cited by 2201DisjointSupSet.sSup · cited by 954SupSet.sSupOrder.Frame · cited by 88Order.FrameIsGreatest.isLUB · cited by 25IsGreatest.isLUBIsLUB.sSup_eq · cited by 17IsLUB.sSup_eqisGreatest_compl · cited by 1isGreatest_complcompl_eq_sSup_disjointCITED BYCITES

Cites8

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

Cited by1

Results whose statement or proof uses this declaration.