∀ {α : Type u_2} {M : Type u_1} [inst : Monoid M] (f : α → M) (x x_1 : FreeMonoid α),
  FreeMonoid.prodAux (List.map f (FreeMonoid.toList (x * x_1))) =
    FreeMonoid.prodAux (List.map f (FreeMonoid.toList x)) * FreeMonoid.prodAux (List.map f (FreeMonoid.toList x_1))