∀ {α : Type u_1} {β : Type u_2} {ι : Type u_3} [inst : TopologicalSpace α] [inst_1 : UniformSpace β] {F : ι → α → β}
  {f : α → β} {s : Set α} {x : α} {p : Filter ι} {g : ι → α},
  ContinuousWithinAt f s x →
    Filter.Tendsto g p (nhdsWithin x s) →
      (∀ u ∈ uniformity β, ∃ t ∈ nhdsWithin x s, ∀ᶠ (n : ι) in p, ∀ y ∈ t, (f y, F n y) ∈ u) →
        Filter.Tendsto (fun n => F n (g n)) p (nhds (f x))