∀ {R : Type u_1} [inst : CommRing R] (M M_1 : Submonoid R) (e_M : M = M_1) {S : Type u_2} [inst_1 : CommRing S]
  [inst_2 : Algebra R S] [inst_3 : IsLocalization M S] (p p_1 : Polynomial S),
  p = p_1 →
    ∀ (i i_1 : ℕ),
      i = i_1 → IsLocalization.coeffIntegerNormalization M p i = IsLocalization.coeffIntegerNormalization M_1 p_1 i_1