Section Operations.
Context {K : AbsRing} {V : NormedModule K}.
Local Ltac plus_grab e :=
repeat rewrite (plus_assoc _ e) -(plus_comm e) -(plus_assoc e).
End Operations.

Lemma filterdiff_mult {K : AbsRing} :
forall {F} {FF : ProperFilter F} (x : K * K),
is_filter_lim F x ->
(forall (n m : K), mult n m = mult m n) ->
filterdiff (fun t : K * K => mult (fst t) (snd t)) F
(fun t => plus (mult (fst t) (snd x)) (mult (fst x) (snd t))).