Theorems · Theorem · general topology
Filter.frequently_mem_iff_neBot
∀ {α : Type u} {l : Filter α} {s : Set α}, (∃ᶠ (x : α) in l, x ∈ s) ↔ (l ⊓ Filter.principal s).NeBot- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 5 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.
Cites6
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
- Filter.NeBotstatement · cited by 853
- Filter.principalstatement · cited by 740
- Filter.Frequentlystatement · cited by 414
- Filter.frequently_iff_neBotproof · cited by 7
Cited by5
Results whose statement or proof uses this declaration.
- Filter.comap_inf_principal_neBot_of_image_memproof · cited by 4
- AnalyticOnNhd.eq_zero_or_eq_zero_of_smul_eq_zeroproof · cited by 1
- IsCompact.exists_clusterPt_of_frequentlyproof · cited by 1
- Filter.cofinite_inf_principal_neBot_iffproof · cited by 1
- Filter.cocardinal_inf_principal_neBot_iffproof · cited by 0