∀ {α : Type u_1} {β : Type u_2} {ι : Type u_4} [inst : TopologicalSpace α] [inst_1 : UniformSpace β] {F : ι → α → β}
  {f : α → β} {p : Filter ι} [LocallyCompactSpace α],
  TendstoLocallyUniformly F f p = ∀ (K : Set α), IsCompact K → TendstoUniformlyOn F f p K