Theorems · Theorem · general topology
Filter.HasBasis.eventually_iff
∀ {α : Type u_1} {ι : Sort u_4} {l : Filter α} {p : ι → Prop} {s : ι → Set α},
l.HasBasis p s → ∀ {q : α → Prop}, (∀ᶠ (x : α) in l, q x) ↔ ∃ i, p i ∧ ∀ ⦃x : α⦄, x ∈ s i → q x- Defined in
- Mathlib.Order.Filter.Bases.Basic
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
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
- Filterstatement and proof · cited by 8,121
- Filter.Eventuallystatement · cited by 3,134
- Filter.HasBasisstatement and proof · cited by 604
- Filter.HasBasis.mem_iffproof · cited by 193
Cited by38
Results whose statement or proof uses this declaration.
- Filter.HasBasis.tendsto_iffproof · cited by 60
- Filter.HasBasis.frequently_iffproof · cited by 16
- Absorbs.exists_posproof · cited by 8
- Filter.eventually_forall_ge_atTopproof · cited by 5
- Filter.HasBasis.limsSup_eq_iInf_sSupproof · cited by 5
- EReal.continuous_toENNRealproof · cited by 4
- Filter.HasBasis.liminf_eq_sSup_iUnion_iInterproof · cited by 4
- MeasureTheory.exists_eLpNorm_indicator_leproof · cited by 3
- absorbs_iff_normproof · cited by 3
- Complex.norm_eventually_eq_of_isLocalMaxproof · cited by 2
- not_differentiableWithinAt_of_deriv_tendsto_atBot_Iioproof · cited by 2
- not_differentiableWithinAt_of_deriv_tendsto_atTop_Ioiproof · cited by 2