∀ {R : Type u_1} [inst : Ring R] {P : Polynomial R} {η : R} (d : ℕ),
  P.natDegree = d + 1 →
    ((Polynomial.X - Polynomial.C η) * P).natDegree = P.natDegree + 1 →
      ((Polynomial.X - Polynomial.C η) * P).nextCoeff = P.coeff d - η * P.coeff (d + 1)