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

Lemma filterdiff_iter_plus_fct {I} {F} {FF : Filter F}
(l : list I) (f : I -> U -> V) df (x : U) :
(forall (j : I), List.In j l -> filterdiff (f j) F (df j)) ->
filterdiff (fun y => iter plus zero l (fun j => f j y)) F
(fun x => iter plus zero l (fun j => df j x)).