∀ {R : Type u_1} (S : Type u_2) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {n : ℕ} (m k : ℕ)
  (hn : n = m + k) (p : Polynomial.MonicDegreeEq R n),
  Polynomial.UniversalFactorizationRing.homEquiv S m k hn p =
    {
      toFun := fun f =>
        ⟨((Polynomial.UniversalFactorizationRing.factor₁ m k hn p).map ↑f,
            (Polynomial.UniversalFactorizationRing.factor₂ m k hn p).map ↑f),
          ⋯⟩,
      invFun := fun q =>
        Algebra.TensorProduct.lift (Algebra.ofId R S)
          (let __RingHom :=
            (↑((MvPolynomial.universalFactorizationMapLiftEquiv R S n m k hn (p.map (algebraMap R S))).symm
                  q)).toRingHom;
          { toRingHom := __RingHom, commutes' := ⋯ })
          ⋯,
      left_inv := ⋯, right_inv := ⋯ }