∀ {α : Type u} {β : Type v} {ι : Type u_1} [inst : PseudoMetricSpace α] [inst_1 : TopologicalSpace β] {F : ι → β → α}
  {f : β → α} {p : Filter ι} {s : Set β},
  TendstoLocallyUniformlyOn F f p s ↔
    ∀ ε > 0, ∀ x ∈ s, ∃ t ∈ nhdsWithin x s, ∀ᶠ (n : ι) in p, ∀ y ∈ t, dist (f y) (F n y) < ε