Theorems · Theorem · general topology
Filter.frequently_iff_neBot
∀ {α : Type u} {l : Filter α} {p : α → Prop}, (∃ᶠ (x : α) in l, p x) ↔ (l ⊓ Filter.principal {x | p x}).NeBot- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Filterstatement and proof · cited by 8,121
- Set.ofPredstatement and proof · cited by 6,101
- Bot.botproof · cited by 4,720
- Filter.NeBotstatement · cited by 853
- Filter.principalstatement and proof · cited by 740
- Filter.Frequentlystatement and proof · cited by 414
- Filter.neBot_iffproof · cited by 27
- Filter.inf_principal_eq_botproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- Filter.frequently_mem_iff_neBotproof · cited by 5
- egauge_ball_le_of_one_lt_normproof · cited by 4
- egauge_univproof · cited by 2
- exists_enorm_ltproof · cited by 1
- frequently_gt_nhdsproof · cited by 1
- frequently_lt_nhdsproof · cited by 1
- exists_enorm_lt'proof · cited by 0