∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : DecidableEq (Associates α)]
  [inst_2 : (p : Associates α) → Decidable (Irreducible p)] {p : Associates α} (hp : Irreducible p)
  (s : Multiset { a // Irreducible a }), p.count ↑s = Multiset.count ⟨p, hp⟩ s