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Theorems · Theorem · order theory

mem_countableSupClosure_iff

∀ {α : Type u_2} {s : Set α} {a : α} [inst : Preorder α],
  a ∈ countableSupClosure s ↔ ∃ A, ∃ (_ : A ⊆ s) (_ : A.Nonempty) (_ : A.Countable), IsLUB A a
Defined in
Mathlib.Order.CountableSupClosed
Cited by
1 results in Mathlib
Foundations
Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Preorder
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Around this declaration

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

upperBounds_countableSupClosure · cited by 1upperBounds_countableSupC…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetPreorder · cited by 7952PreorderSet.Nonempty · cited by 2627Set.NonemptySet.Countable · cited by 545Set.CountableClosureOperator · cited by 371ClosureOperatorIsLUB · cited by 280IsLUBcountableSupClosure · cited by 21countableSupClosuremem_countableSupClosure_iffCITED BYCITES

Cites8

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Cited by1

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