End Diff_comp2'.
Context {W : NormedModule K}.

(* Specifications: *)
Lemma filterdiff_comp'_2 :
forall (f : T -> U) (g : T -> V) (h : U -> V -> W) x (lf : T -> U) (lg : T -> V)
(lh : U -> V -> W),
filterdiff f (locally x) lf ->
filterdiff g (locally x) lg ->
filterdiff (fun t => h (fst t) (snd t)) (locally (f x,g x)) (fun t => lh (fst t) (snd t)) ->
filterdiff (fun y : T => h (f y) (g y)) (locally x) (fun y : T => lh (lf y) (lg y)).
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).