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

Lemma ex_filterdiff_scal_fct x (f : U -> K) (g : U -> V) :
(forall (n m : K), mult n m = mult m n) ->
ex_filterdiff f (locally x) -> ex_filterdiff g (locally x) ->
ex_filterdiff (fun t => scal (f t) (g t)) (locally x).