Poly Fold step

lemma polyFold_step {f : F[X]} {k : ℕ} {r : F} (hk : 0 < k) (hf : k ≤ f.natDegree) :    polyFold f k r =      Polynomial.C ((f %ₘ X^k).eval r) + X * polyFold (f /ₘ X^k) k r := by  unfold polyFold  have h_deg_q : 0 < (X^k : F[X]).degree := by    rw [Polynomial.degree_X_pow]; exact_mod_cast hk  have h_deg_f : (X^k : F[X]).degree ≤ f.degree := by    rw [Polynomial.degree_X_pow]    have hf0 : f ≠ 0 := by      rintro rfl; simp at hf; omega    rw [Polynomial.degree_eq_natDegree hf0]; exact_mod_cast hf  rw [folding_polynomial_def_ind_case h_deg_f h_deg_q]  rw [Polynomial.eval_add, Polynomial.eval_mul, Polynomial.eval_C, eval_C_map_C]  rw [show f / X^k = f /ₘ X^k from        (divByMonic_eq_div f (Polynomial.monic_X_pow k)).symm,      show f % X^k = f %ₘ X^k from        (modByMonic_eq_mod f (Polynomial.monic_X_pow k)).symm]