∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α]
  [inst_2 : DecidableEq (Associates α)] [inst_3 : (p : Associates α) → Decidable (Irreducible p)] {a p : α},
  a ≠ 0 → Irreducible p → ((Associates.mk p).count (Associates.mk a).factors ≠ 0 ↔ p ∣ a)