∀ {ι : Type u_1} {α : Type u_6} {β : Type u_8} {γ : Type u_10} [uα : UniformSpace α] [uβ : UniformSpace β]
  [uγ : UniformSpace γ] {F : ι → β → α} {S : Set β} {u : α → γ},
  IsUniformInducing u → (UniformEquicontinuousOn F S ↔ UniformEquicontinuousOn ((fun x => u ∘ x) ∘ F) S)