Theorems · Theorem · order theory
CountableSupClosed.sSup_mem
∀ {α : Type u_2} {s : Set α} [inst : CompleteLattice α],
CountableSupClosed s → ∀ {A : Set α}, A.Countable → A.Nonempty → (∀ a ∈ A, a ∈ s) → sSup A ∈ s- Defined in
- Mathlib.Order.CountableSupClosed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.Elemproof · cited by 7,166
- Set.Nonemptystatement and proof · cited by 2,627
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupstatement · cited by 954
- Countableproof · cited by 633
- Set.Countablestatement and proof · cited by 545
- sSup_eq_iSup'proof · cited by 38
- CountableSupClosedstatement and proof · cited by 27
- Set.nonempty_coe_sortproof · cited by 23
- CountableSupClosed.iSup_memproof · cited by 3
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.