End Diff.
Section Diff_comp.
Context {K : AbsRing} {U V W : NormedModule K}.

(* Specifications: *)
Lemma filterdiff_comp
{F} {FF : Filter F} f g (lf : U -> V) (lg : V -> W) :
filterdiff f F lf -> filterdiff g (filtermap f F) lg
-> filterdiff (fun y => g (f y)) F (fun y => lg (lf y)).
Lemma ex_filterdiff_comp
{F} {FF : Filter F} (f : U -> V) (g : V -> W) :
ex_filterdiff f F -> ex_filterdiff g (filtermap f F)
-> ex_filterdiff (fun y => g (f y)) F.
Lemma filterdiff_comp'
f g x (lf : U -> V) (lg : V -> W) :
filterdiff f (locally x) lf -> filterdiff g (locally (f x)) lg
-> filterdiff (fun y => g (f y)) (locally x) (fun y => lg (lf y)).
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).