Theorems · Theorem · general topology
Ultrafilter.exists_ultrafilter_of_finite_inter_nonempty
∀ {α : Type u} (S : Set (Set α)), (∀ (T : Finset (Set α)), ↑T ⊆ S → (⋂₀ ↑T).Nonempty) → ∃ F, S ⊆ (↑F).sets- Defined in
- Mathlib.Order.Filter.Ultrafilter.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Set.Nonemptystatement and proof · cited by 2,627
- Set.sInterstatement and proof · cited by 225
- Ultrafilterstatement · cited by 193
- Ultrafilter.toFilterstatement · cited by 172
- Filter.setsstatement · cited by 56
- Filter.generateproof · cited by 30
- Ultrafilter.ofproof · cited by 15
- Ultrafilter.of_leproof · cited by 15
Cited by1
Results whose statement or proof uses this declaration.
- Compactum.str_eq_of_le_nhdsproof · cited by 2