∀ {M : Type u_1} [inst : CommMonoidWithZero M] [UniqueFactorizationMonoid M] {q : Associates M} {n : ℕ},
  n ≠ 0 →
    ∀ {c : Fin (n + 1) → Associates M},
      StrictMono c → (∀ {r : Associates M}, r ≤ q ↔ ∃ i, r = c i) → q ≠ 0 → q = c 1 ^ n