Theorems · Theorem · general topology
Ultrafilter.compl_mem_iff_notMem
∀ {α : Type u} {f : Ultrafilter α} {s : Set α}, sᶜ ∈ f ↔ s ∉ f- Defined in
- Mathlib.Order.Filter.Ultrafilter.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.complstatement · cited by 2,925
- compl_complproof · cited by 229
- Ultrafilterstatement and proof · cited by 193
- Ultrafilter.compl_notMem_iffproof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- Compactum.str_eq_of_le_nhdsproof · cited by 2
- isCompact_generateFromproof · cited by 2
- Ultrafilter.mem_or_compl_memproof · cited by 2
- ultrafilter_isClosed_basicproof · cited by 2
- Compactum.isClosed_iffproof · cited by 1
- Ultrafilter.sdiff_mem_iffproof · cited by 1
- Filter.compl_mem_hyperfilter_of_finiteproof · cited by 1
- ConditionallyCompleteLinearOrder.isCompact_Iccproof · cited by 0
- Ultrafilter.eventually_notproof · cited by 0