Theorems · Theorem · general topology
Filter.notMem_hyperfilter_of_finite
∀ {α : Type u} [inst : Infinite α] {s : Set α}, s.Finite → s ∉ Filter.hyperfilter α- Defined in
- Mathlib.Order.Filter.Ultrafilter.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Infinite
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
- Compl.complproof · cited by 2,925
- Set.Finitestatement and proof · cited by 1,814
- Infinitestatement and proof · cited by 352
- Ultrafilterstatement · cited by 193
- Filter.hyperfilterstatement and proof · cited by 30
- Set.Finite.compl_mem_cofiniteproof · cited by 14
- Filter.compl_notMemproof · cited by 6
- Filter.hyperfilter_le_cofiniteproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Set.Finite.notMem_hyperfilterproof · cited by 1