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 ex_filterdiff_comp' (f : U -> V) (g : V -> W) x : ex_filterdiff f (locally x) -> ex_filterdiff g (locally (f x)) -> ex_filterdiff (fun y => g (f y)) (locally x).