Theorems · Theorem · general topology
Filter.compl_notMem
∀ {α : Type u} {f : Filter α} {s : Set α} [f.NeBot], s ∈ f → sᶜ ∉ f- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Filter.NeBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Filterstatement and proof · cited by 8,121
- Compl.complstatement and proof · cited by 2,925
- Filter.NeBotstatement and proof · cited by 853
- Filter.inter_memproof · cited by 153
- Set.Nonempty.ne_emptyproof · cited by 65
- Filter.nonempty_of_memproof · cited by 36
- Set.inter_compl_selfproof · cited by 17
Cited by6
Results whose statement or proof uses this declaration.
- Filter.Eventually.frequentlyproof · cited by 44
- isCompact_of_finite_subcoverproof · cited by 5
- Ultrafilter.compl_notMem_iffproof · cited by 4
- isLindelof_of_countable_subcoverproof · cited by 4
- MeromorphicOn.circleAverage_log_normproof · cited by 3
- Filter.notMem_hyperfilter_of_finiteproof · cited by 1