∀ {R : Type u} [inst : Semiring R] {S : Type v} [inst_1 : Semiring S] {f : R →+* S} {s : S} {n : ℕ},
  (Polynomial.monomial n) s ∈ Polynomial.lifts f →
    ∃ q, Polynomial.map f q = (Polynomial.monomial n) s ∧ q.degree = ((Polynomial.monomial n) s).degree