Theorems · Theorem · general topology
Filter.Eventually.frequently
∀ {α : Type u} {f : Filter α} [f.NeBot] {p : α → Prop}, (∀ᶠ (x : α) in f, p x) → ∃ᶠ (x : α) in f, p x- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 44 results in Mathlib
- Foundations
- Depth 59 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.
Cites5
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
- Filter.Eventuallystatement and proof · cited by 3,134
- Filter.NeBotstatement and proof · cited by 853
- Filter.Frequentlystatement · cited by 414
- Filter.compl_notMemproof · cited by 6
Cited by44
Results whose statement or proof uses this declaration.
- Filter.Eventually.existsproof · cited by 168
- IsClosed.mem_of_tendstoproof · cited by 32
- meromorphicOrderAt_eq_int_iffproof · cited by 31
- Filter.Frequently.of_forallproof · cited by 25
- meromorphicOrderAt_eq_top_iffproof · cited by 20
- mem_closure_of_tendstoproof · cited by 19
- le_of_tendsto_of_tendstoproof · cited by 13
- mem_tangentConeAt_of_seqproof · cited by 8
- ClusterPt.limsSupproof · cited by 4
- Filter.comap_inf_principal_neBot_of_image_memproof · cited by 4
- HasDerivWithinAt.liminf_right_slope_norm_leproof · cited by 3
- AnalyticAt.exists_eventuallyEq_pow_smul_nonzero_iffproof · cited by 3