∀ {R : Type u} {A : Type z} {B : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
  [inst_3 : Algebra R A] [inst_4 : Algebra R B] (f : A →ₐ[R] B), ↑(Polynomial.mapAlgHom f) = Polynomial.mapRingHom ↑f