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_comp' f g x (lf : U -> V) (lg : V -> W) : filterdiff f (locally x) lf -> filterdiff g (locally (f x)) lg -> filterdiff (fun y => g (f y)) (locally x) (fun y => lg (lf y)).