Theorems · Theorem · general topology
Filter.Eventually.mp
∀ {α : Type u} {p q : α → Prop} {f : Filter α},
(∀ᶠ (x : α) in f, p x) → (∀ᶠ (x : α) in f, p x → q x) → ∀ᶠ (x : α) in f, q x- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 78 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.mp_memproof · cited by 1,537
Cited by78
Results whose statement or proof uses this declaration.
- Filter.Eventually.monoproof · cited by 646
- Filter.Frequently.and_eventuallyproof · cited by 49
- Filter.EventuallyLE.transproof · cited by 27
- Filter.EventuallyLE.antisymmproof · cited by 23
- Filter.Frequently.mpproof · cited by 12
- Filter.Eventually.congrproof · cited by 6
- MeasureTheory.condExp_smulproof · cited by 5
- MeasureTheory.AECover.interproof · cited by 5
- Filter.EventuallyEq.fderivWithin'proof · cited by 5
- Filter.EventuallyEq.prodMkproof · cited by 4
- TendstoLocallyUniformlyOn.congr_inseparable_rightproof · cited by 4
- Filter.EventuallyLE.isMaxFilterproof · cited by 4