∀ {α : Type u} {β : Type v} [uniformSpace : UniformSpace α] [inst : UniformSpace β] {f : Filter β} {m : α → β},
  Cauchy f →
    Filter.comap (fun p => (m p.1, m p.2)) (uniformity β) ≤ uniformity α →
      ∀ [(Filter.comap m f).NeBot], Cauchy (Filter.comap m f)