∀ {ι : Type u_1} {X : Type u_3} {α : Type u_6} {β : Type u_8} [tX : TopologicalSpace X] [uα : UniformSpace α]
  [uβ : UniformSpace β] {F : ι → X → α} {S : Set X} {u : α → β},
  IsUniformInducing u → (EquicontinuousOn F S ↔ EquicontinuousOn ((fun x => u ∘ x) ∘ F) S)