∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {ι : Type u_4} [inst : UniformSpace β] {F : ι → α → β} {s : Set α}
  {p : Filter ι} [inst_1 : UniformSpace γ] {g : β → γ},
  UniformContinuous g → UniformCauchySeqOn F p s → UniformCauchySeqOn (fun n => g ∘ F n) p s