∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) [inst_1 : I.IsPrime] (x : Polynomial I.ResidueField)
  (r : Polynomial R),
  Polynomial.map (Ideal.Quotient.mk I) r = IsLocalization.integerNormalization (nonZeroDivisors (R ⧸ I)) x →
    ∃ s ∉ I, Polynomial.map (algebraMap R I.ResidueField) r = s • x