∀ {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},
  0 ∈ {x | x ∈ I ∧ ∀ (n : ℕ), f (hI.dpow n x) = hJ.dpow n (f x)}