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Theorems · Theorem · order theory

CountableInfClosed.sInter

∀ {α : Type u_2} {S : Set (Set α)} [inst : LE α], (∀ s ∈ S, CountableInfClosed s) → CountableInfClosed (⋂₀ S)
Defined in
Mathlib.Order.CountableSupClosed
Cited by
1 results in Mathlib
Foundations
Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LE
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Around this declaration

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

CountableInfClosed.iInter · cited by 0CountableInfClosed.iInterSet · cited by 53352SetSet.Nonempty · cited by 2627Set.NonemptySet.Countable · cited by 545Set.CountableSet.sInter · cited by 225Set.sInterIsGLB · cited by 213IsGLBCountableInfClosed · cited by 27CountableInfClosedCountableInfClosed.isGLB_mem · cited by 10CountableInfClosed.isGLB_…Set.mem_sInter · cited by 7Set.mem_sInterSet.subset_sInter_iff · cited by 5Set.subset_sInter_iffCountableInfClosed.sInterCITED BYCITES

Cites9

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.