∀ {σ : Type u_1} {R : Type u_2} [inst : CommSemiring R] (a : σ → R) (x y : MvPowerSeries σ R),
  (fun n => (n.prod fun s m => a s ^ m) * (MvPowerSeries.coeff n) (x + y)) =
    (fun n => (n.prod fun s m => a s ^ m) * (MvPowerSeries.coeff n) x) + fun n =>
      (n.prod fun s m => a s ^ m) * (MvPowerSeries.coeff n) y