Definition nat_to_ring (n : nat) : K :=
  sum_n_m (fun _ => one) 1 n.

Lemma filterdiff_pow_n {K : AbsRing} (x : K) (n : nat) : (forall a b : K, mult a b = mult b a) -> filterdiff (fun y : K => pow_n y n) (locally x) (fun y : K => scal y (mult (nat_to_ring n) (pow_n x (pred n)))).