Theorems · Theorem · general topology
Filter.eventually_smallSets_forall
∀ {α : Type u_1} {l : Filter α} {p : α → Prop}, (∀ᶠ (s : Set α) in l.smallSets, ∀ x ∈ s, p x) ↔ ∀ᶠ (x : α) in l, p x- Defined in
- Mathlib.Order.Filter.SmallSets
- Cited by
- 3 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.
Cites6
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 and proof · cited by 3,134
- Filter.smallSetsstatement and proof · cited by 89
- inf_top_eqproof · cited by 30
- Filter.eventually_smallSets_eventuallyproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Filter.eventually_smallSets_subsetproof · cited by 3
- Filter.Eventually.smallSetsproof · cited by 2
- Filter.Eventually.of_smallSetsproof · cited by 0