Definition filterdiff (f : U -> V) F (l : U -> V) :=
  is_linear l /\ forall x, is_filter_lim F x ->
  is_domin F (fun y : U => minus y x) (fun y => minus (minus (f y) (f x)) (l (minus y x))).Definition ex_filterdiff (f : U -> V) F :=
  exists (l : U -> V), filterdiff f F l.

Lemma filterdiff_scal_l_fct : forall {F} {FF : Filter F} (x : V) (f : U -> K) lf, filterdiff f F lf -> filterdiff (fun u => scal (f u) x) F (fun u => scal (lf u) x).