{A : Type u_1} →
  {B : Type u_2} →
    [inst : CommSemiring A] →
      {I : Ideal A} →
        [inst_1 : CommSemiring B] →
          {J : Ideal B} → {e : A ≃+* B} → Ideal.map e I = J → DividedPowers I → DividedPowers J