Theorems · Theorem · general topology
Filter.Eventually.exists
∀ {α : Type u} {p : α → Prop} {f : Filter α} [f.NeBot], (∀ᶠ (x : α) in f, p x) → ∃ x, p x- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 168 results in Mathlib
- Foundations
- Depth 60 from the axioms, rests on 700 definitions · 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.Eventually.frequentlyproof · cited by 44
- Filter.Frequently.existsproof · cited by 32
Cited by168
Results whose statement or proof uses this declaration.
- Filter.atTop_neBot_iffproof · cited by 9
- Filter.IsBounded.isCobounded_flipproof · cited by 8
- LieModule.genWeightSpace_chainTopCoeff_add_one_nsmul_addproof · cited by 6
- Filter.tendsto_iff_seq_tendstoproof · cited by 5
- MeasureTheory.MeasurePreserving.skew_productproof · cited by 5
- interior_subset_gauge_lt_oneproof · cited by 5
- MeasureTheory.exists_Lp_halfproof · cited by 4
- Monotone.measure_iInterproof · cited by 4
- Filter.HasAntitoneBasis.subbasis_with_relproof · cited by 4
- Monotone.tendstoLocallyUniformly_of_forall_tendstoproof · cited by 4
- summable_geometric_iff_norm_lt_oneproof · cited by 4
- MeasureTheory.addHaar_image_le_mul_of_det_ltproof · cited by 4