∀ {R : Type u} [inst : CommRing R] {𝓟 : Ideal R} {f : Polynomial R} {S : Type v} [inst_1 : CommRing S]
  [inst_2 : Algebra R S],
  f.IsWeaklyEisensteinAt 𝓟 →
    ∀ {x : S},
      (Polynomial.aeval x) f = 0 →
        f.Monic → ∀ (i : ℕ), (Polynomial.map (algebraMap R S) f).natDegree ≤ i → x ^ i ∈ Ideal.map (algebraMap R S) 𝓟