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'_2 : forall (f : T -> U) (g : T -> V) (h : U -> V -> W) x, ex_filterdiff f (locally x) -> ex_filterdiff g (locally x) -> ex_filterdiff (fun t => h (fst t) (snd t)) (locally (f x,g x)) -> ex_filterdiff (fun y : T => h (f y) (g y)) (locally x).