∀ {α : Type u_1} {β : Type u_3} {γ : Type u_2} [inst : UniformSpace β] {𝔖 : Set (Set α)} [inst_1 : UniformSpace γ]
  (e : γ ≃ᵤ β), UniformContinuous (⇑(UniformOnFun.ofFun 𝔖) ∘ (fun x => ⇑e.toEquiv ∘ x) ∘ ⇑(UniformOnFun.toFun 𝔖))