∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {ι : Type u_4} [inst : TopologicalSpace α] [inst_1 : UniformSpace β]
  {F : ι → α → β} {f : α → β} {s : Set α} {p : Filter ι} [inst_2 : TopologicalSpace γ] {t : Set γ},
  TendstoLocallyUniformlyOn F f p s →
    ∀ (g : γ → α), Set.MapsTo g t s → ContinuousOn g t → TendstoLocallyUniformlyOn (fun n => F n ∘ g) (f ∘ g) p t