{α : Type ua} →
  {β : Type ub} →
    [inst : UniformSpace α] →
      [inst_1 : UniformSpace β] →
        {f : α → β} →
          {motive : IsUniformInducing f → Sort u} →
            ((comap_uniformity : Filter.comap (fun x => (f x.1, f x.2)) (uniformity β) = uniformity α) → motive ⋯) →
              (t : IsUniformInducing f) → motive t