∀ {σ : Type u_1} {R : Type u_2} [inst : CommRing R] (n : σ →₀ ℕ) (p q : MvPolynomial σ R)
  (motive : (∃ m r, m ≤ n ∧ r ∣ q ∧ p = (MvPolynomial.monomial m) 1 * r) → Prop)
  (x : ∃ m r, m ≤ n ∧ r ∣ q ∧ p = (MvPolynomial.monomial m) 1 * r),
  (∀ (m : σ →₀ ℕ) (r : MvPolynomial σ R) (hmn : m ≤ n) (hrq : r ∣ q) (hp : p = (MvPolynomial.monomial m) 1 * r),
      motive ⋯) →
    motive x