∀ {R : Type u_4} (σ : Type u_1) [inst : CommSemiring R] {A₁ : Type u_2} {A₂ : Type u_3} [inst_1 : CommSemiring A₁]
  [inst_2 : CommSemiring A₂] [inst_3 : Algebra R A₁] [inst_4 : Algebra R A₂] (e : A₁ ≃ₐ[R] A₂)
  (x y : MvPolynomial σ A₁),
  (↑↑(MvPolynomial.mapAlgHom ↑e).toRingHom).toFun (x * y) =
    (↑↑(MvPolynomial.mapAlgHom ↑e).toRingHom).toFun x * (↑↑(MvPolynomial.mapAlgHom ↑e).toRingHom).toFun y