Theorems · Theorem · order theory
Set.exists_dissipate_eq_empty_iff_of_directed
∀ {α : Type u_1} {s : ℕ → Set α}, Directed (fun x1 x2 => x1 ⊇ x2) s → ((∃ n, Set.dissipate s n = ∅) ↔ ∃ n, s n = ∅)- Defined in
- Mathlib.Order.SetDissipate
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.Nonemptyproof · cited by 2,627
- le_rflproof · cited by 1,558
- Directedstatement and proof · cited by 213
- Set.Nonempty.monoproof · cited by 88
- Set.dissipatestatement and proof · cited by 24
- Set.subset_eq_emptyproof · cited by 6
- Set.dissipate_subsetproof · cited by 2
- Set.exists_subset_dissipate_of_directedproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- isCompactSystem_iff_of_directedproof · cited by 1