(** ** Exchange limit and integral *)

Lemma filterlim_RInt {U} {V : CompleteNormedModule R_AbsRing} :
forall (f : U -> R -> V) (a b : R) F (FF : ProperFilter F)
g h,
(forall x, is_RInt (f x) a b (h x))
-> (filterlim f F (locally g))
-> exists If, filterlim h F (locally If) /\ is_RInt g a b If.