Theorems · Theorem · general topology
Filter.frequently_iff
∀ {α : Type u} {f : Filter α} {P : α → Prop}, (∃ᶠ (x : α) in f, P x) ↔ ∀ {U : Set α}, U ∈ f → ∃ x ∈ U, P x- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Set.ofPredproof · cited by 6,101
- Filter.Frequentlystatement · cited by 414
- Function.Surjective.forallproof · cited by 214
- Function.Bijective.surjectiveproof · cited by 114
- Set.ofPred_bijectiveproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- continuous_cfcₙHomSuperset_leftproof · cited by 1
- Metric.forall_of_forall_mem_closedBallproof · cited by 1
- continuous_cfcHomSuperset_leftproof · cited by 1
- Metric.forall_of_forall_mem_ballproof · cited by 0