{A : Type u_1} →
  {B : Type u_2} →
    [inst : CommSemiring A] →
      [inst_1 : CommSemiring B] →
        {I : Ideal A} →
          {J : Ideal B} →
            {hI : DividedPowers I} →
              {hJ : DividedPowers J} →
                {f : A →+* B} →
                  {motive : hI.IsDPMorphism hJ f → Sort u} →
                    ((ideal_comp : Ideal.map f I ≤ J) →
                        (dpow_comp : ∀ {n : ℕ}, ∀ a ∈ I, hJ.dpow n (f a) = f (hI.dpow n a)) → motive ⋯) →
                      (t : hI.IsDPMorphism hJ f) → motive t