∀ {S : Type u_3} {A : Type u_2} {B : Type u_1} [inst : CommSemiring S] [inst_1 : Semiring A] [inst_2 : Semiring B]
  [inst_3 : Algebra S A] [inst_4 : Algebra S B] (f : A ≃ₐ[S] B) (x y : A),
  (↑f).toFun (x + y) = (↑f).toFun x + (↑f).toFun y