∀ {n : Type u_1} {R : Type u_2} [inst : CommRing R] {f : MvPolynomial n R} {d : n →₀ ℕ} {i : n},
  MvPolynomial.coeff d f ≠ 0 →
    (∀ (k : n →₀ ℕ),
        MvPolynomial.coeff k
            (f - (MvPolynomial.monomial (Finsupp.erase i d)) (MvPolynomial.coeff d f) * MvPolynomial.X i) =
          if d = k then 0 else MvPolynomial.coeff k f) →
      ¬(MvPolynomial.monomial (Finsupp.erase i d)) (MvPolynomial.coeff d f) = 0