∀ {M₀ : Type u_1} [inst : CommMonoidWithZero M₀] {p : Associates M₀} (motive : p ≤ Multiset.prod 0 → Prop)
  (x : p ≤ Multiset.prod 0), (∀ (w : Associates M₀) (eq : Multiset.prod 0 = p * w), motive ⋯) → motive x