∀ {R : Type u_1} [inst : CommMonoidWithZero R] (n : R) (motive : (∃ p k, Prime p ∧ 0 < k ∧ p ^ k = n) → Prop)
  (x : ∃ p k, Prime p ∧ 0 < k ∧ p ^ k = n),
  (∀ (p : R) (k : ℕ) (hp : Prime p) (hk : 0 < k) (hn : p ^ k = n), motive ⋯) → motive x