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Theorems · Theorem · logic and foundations

IsClub.isLUB_mem

∀ {α : Type v} {s t : Set α} {x : α} [inst : LinearOrder α], IsClub s → t ⊆ s → t.Nonempty → IsLUB t x → x ∈ s
Defined in
Mathlib.SetTheory.Cardinal.Cofinality.Club
Cited by
2 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext
Assumes
LinearOrder
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Around this declaration

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

IsClub.sInter · cited by 2IsClub.sInterIsClub.csSup_mem · cited by 0IsClub.csSup_memSet · cited by 53352SetLinearOrder · cited by 8572LinearOrderSet.Nonempty · cited by 2627Set.NonemptyIsLUB · cited by 280IsLUBIsClub · cited by 30IsClubIsClub.dirSupClosed · cited by 4IsClub.dirSupClosedDirectedOn.of_linearOrder · cited by 1DirectedOn.of_linearOrderIsClub.isLUB_memCITED BYCITES

Cites7

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.