∀ {R : Type u_2} [inst : CommRing R] {S : Type u_1} [inst_1 : CommRing S] {f : R →+* S} {p : Ideal R} {P : Ideal S},
  (∃ n, ∀ (k : ℕ), Ideal.map f p ≤ P ^ k → k ≤ n) → ∃ n, ∀ (k : ℕ), Ideal.map f p ≤ P ^ k → k ≤ n