End Operations.

(* Specifications: *)
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))).
Lemma ex_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) ->
ex_filterdiff (fun t : K * K => mult (fst t) (snd t)) F.