∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {s : S} (n : ℕ),
  (minpoly R s).natDegree ≤ n → ∀ i < (minpoly R s).natDegree, n - (minpoly R s).natDegree + i < n