Theorems · Theorem · order theory
CountableSupClosed.iSup_mem
∀ {ι : Sort u_1} {α : Type u_2} {s : Set α} [inst : CompleteLattice α] [Countable ι] [Nonempty ι],
CountableSupClosed s → ∀ {A : ι → α}, (∀ (n : ι), A n ∈ s) → ⨆ n, A n ∈ s- Defined in
- Mathlib.Order.CountableSupClosed
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.rangeproof · cited by 4,705
- iSupstatement and proof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- Countablestatement and proof · cited by 633
- Nonempty.someproof · cited by 340
- Set.countable_rangeproof · cited by 31
- CountableSupClosedstatement and proof · cited by 27
- CountableSupClosed.isLUB_memproof · cited by 10
- isLUB_iSupproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- mem_countableSupClosure_iff_iSupproof · cited by 1
- iSup_mem_countableSupClosureproof · cited by 0
- CountableSupClosed.sSup_memproof · cited by 0