∀ {α : Type u} {β : Type v} [uniformSpace : UniformSpace α] {γ : Type u_1} {δ : Type u_2} [inst : UniformSpace β]
  [inst_1 : Preorder γ] [inst_2 : Preorder δ] {u : γ → α} {v : δ → β},
  CauchySeq u → CauchySeq v → CauchySeq (Prod.map u v)