∀ {α : Type u_1} {R : Type u_2} [inst : CommRing R] (F : Multiplicative (Multiset α) →* R)
  (x y : Multiplicative (Multiset α)),
  (Multiset.map (fun x => F (Multiplicative.ofAdd {x})) (Multiplicative.toAdd (x * y))).prod =
    (Multiset.map (fun x => F (Multiplicative.ofAdd {x})) x).prod *
      (Multiset.map (fun x => F (Multiplicative.ofAdd {x})) y).prod