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

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)).