End Diff_comp.
Section Diff_comp2.
Context {K : AbsRing} {T U V : NormedModule K}.
Section Diff_comp2'.
Context {W : NormedModule K}.

(* Specifications: *)
Lemma filterdiff_comp_2
{F : (T -> Prop) -> Prop} {FF : Filter F} :
forall (f : T -> U) (g : T -> V) (h : U -> V -> W) (lf : T -> U) (lg : T -> V)
(lh : U -> V -> W),
filterdiff f F lf ->
filterdiff g F lg ->
filterdiff (fun t => h (fst t) (snd t)) (filtermap (fun t => (f t,g t)) F) (fun t => lh (fst t) (snd t)) ->
filterdiff (fun y : T => h (f y) (g y)) F (fun y : T => lh (lf y) (lg y)).
Lemma ex_filterdiff_comp_2
{F : (T -> Prop) -> Prop} {FF : Filter F} :
forall (f : T -> U) (g : T -> V) (h : U -> V -> W),
ex_filterdiff f F ->
ex_filterdiff g F ->
ex_filterdiff (fun t => h (fst t) (snd t)) (filtermap (fun t => (f t,g t)) F) ->
ex_filterdiff (fun y : T => h (f y) (g y)) F.