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

Lemma ex_filterdiff_mult_fct {K : AbsRing} {U : NormedModule K}
(f g : U -> K) x :
(forall (n m : K), mult n m = mult m n) ->
ex_filterdiff f (locally x) -> ex_filterdiff g (locally x)
-> ex_filterdiff (fun t => mult (f t) (g t)) (locally x).