∀ {α : Type u_1} {β : Type u_2} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β] [inst_2 : Zero α]
  [inst_3 : Zero β] [inst_4 : SMul α β] [IsBoundedSMul α β] {X : Type u_3} {ι : Type u_4} [inst_6 : TopologicalSpace X]
  {s : Set X} {F : ι → X → α} {G : ι → X → β} {f : X → α} {g : X → β} {l : Filter ι},
  TendstoLocallyUniformlyOn F f l s →
    TendstoLocallyUniformlyOn G g l s →
      ContinuousOn f s →
        ContinuousOn g s → TendstoLocallyUniformlyOn (fun i i_1 => F i i_1 • G i i_1) (fun i => f i • g i) l s