Theorems · Theorem · general topology
Ultrafilter.compl_notMem_iff
∀ {α : Type u} {f : Ultrafilter α} {s : Set α}, sᶜ ∉ f ↔ s ∈ f- Defined in
- Mathlib.Order.Filter.Ultrafilter.Defs
- Cited by
- 4 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.
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
- Bot.botproof · cited by 4,720
- Compl.complstatement and proof · cited by 2,925
- Filter.principalproof · cited by 740
- compl_complproof · cited by 229
- Ultrafilterstatement and proof · cited by 193
- Ultrafilter.toFilterproof · cited by 172
- Filter.le_principal_iffproof · cited by 87
- Filter.compl_notMemproof · cited by 6
- Ultrafilter.le_of_inf_neBotproof · cited by 3
- Filter.mem_of_eq_botproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Ultrafilter.compl_mem_iff_notMemproof · cited by 9
- Ultrafilter.frequently_iff_eventuallyproof · cited by 1
- isProperMap_iff_isClosedMap_ultrafilterproof · cited by 1
- isProperMap_iff_isClosedMap_filterproof · cited by 0