∀ {𝕜₁ : Type u_4} {𝕜₂ : Type u_1} [inst : NormedField 𝕜₁] [inst_1 : NormedField 𝕜₂] (σ : 𝕜₁ →+* 𝕜₂) (E : Type u_2)
  (F : Type u_3) [inst_2 : AddCommGroup E] [inst_3 : TopologicalSpace E] [inst_4 : Module 𝕜₁ E]
  [inst_5 : AddCommGroup F] [inst_6 : TopologicalSpace F] [inst_7 : Module 𝕜₂ F] [inst_8 : IsTopologicalAddGroup F]
  [inst_9 : ContinuousConstSMul 𝕜₂ F] (x y : E →SWOT[σ] F),
  (fun x_1 =>
      match x_1 with
      | (x_2, y_1) => y_1 ((x + y) x_2)) =
    (fun x_1 =>
        match x_1 with
        | (x_2, y) => y (x x_2)) +
      fun x =>
      match x with
      | (x, y_1) => y_1 (y x)