Theorems · Theorem · general topology
Ultrafilter.eq_pure_of_finite_mem
∀ {α : Type u} {f : Ultrafilter α} {s : Set α}, s.Finite → s ∈ f → ∃ x ∈ s, f = pure x- Defined in
- Mathlib.Order.Filter.Ultrafilter.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Finitestatement and proof · cited by 1,814
- Ultrafilterstatement and proof · cited by 193
- Set.biUnion_of_singletonproof · cited by 43
- Filter.le_pure_iffproof · cited by 11
- Ultrafilter.eq_of_leproof · cited by 3
- Ultrafilter.finite_biUnion_mem_iffproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Ultrafilter.eq_pure_of_finiteproof · cited by 0
- Ultrafilter.le_cofinite_or_eq_pureproof · cited by 0