Section Operations_fct.
Context {K : AbsRing} {U V : NormedModule K}.

Lemma filterdiff_scal_fct x (f : U -> K) (g : U -> V) lf lg :
(forall (n m : K), mult n m = mult m n) ->
filterdiff f (locally x) lf -> filterdiff g (locally x) lg ->
filterdiff (fun t => scal (f t) (g t)) (locally x)
(fun t => plus (scal (lf t) (g x)) (scal (f x) (lg t))).