∀ {A : Type u_1} [inst : CommSemiring A] {I : Ideal A} (hI hI_1 : DividedPowers I) (e_hI : hI = hI_1) {J : Ideal A}
  (hJ : hI.IsSubDPIdeal J) [inst_1 : (x : A) → Decidable (x ∈ J)],
  DividedPowers.IsSubDPIdeal.dividedPowers hI hJ = DividedPowers.IsSubDPIdeal.dividedPowers hI_1 ⋯