∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] {A : Type u_2} {B : Type u_3} [inst_1 : CommSemiring A]
  [inst_2 : CommSemiring B] [inst_3 : Algebra R A] [inst_4 : Algebra R B] {f g : MvPolynomial σ A →ₐ[R] B},
  f.comp (IsScalarTower.toAlgHom R A (MvPolynomial σ A)) = g.comp (IsScalarTower.toAlgHom R A (MvPolynomial σ A)) →
    (∀ (i : σ), f (MvPolynomial.X i) = g (MvPolynomial.X i)) → f = g