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_ext_locally (f g : U -> V) (x : U) (l : U -> V) : locally x (fun y => f y = g y) -> filterdiff f (locally x) l -> filterdiff g (locally x) l.