∀ (𝕜 : Type u_1) [inst : NontriviallyNormedField 𝕜] {M₁ : Type u_5} {M₂ : Type u_6} {M₃ : Type u_7} {M₄ : Type u_8}
  [inst_1 : SeminormedAddCommGroup M₁] [inst_2 : NormedSpace 𝕜 M₁] [inst_3 : SeminormedAddCommGroup M₂]
  [inst_4 : NormedSpace 𝕜 M₂] [inst_5 : SeminormedAddCommGroup M₃] [inst_6 : NormedSpace 𝕜 M₃]
  [inst_7 : SeminormedAddCommGroup M₄] [inst_8 : NormedSpace 𝕜 M₄] {X : Type u_9} [inst_9 : TopologicalSpace X]
  {f : X → M₁ →L[𝕜] M₂} {g : X → M₃ →L[𝕜] M₄}, Continuous f → Continuous g → Continuous fun x => (f x).prodMap (g x)