Definition is_RInt_gen (f : R -> V) (Fa Fb : (R -> Prop) -> Prop) (l : V) :=
  filterlimi (fun ab => is_RInt f (fst ab) (snd ab)) (filter_prod Fa Fb) (locally l).Definition ex_RInt_gen (f : R -> V) (Fa Fb : (R -> Prop) -> Prop) :=
  exists l : V, is_RInt_gen f Fa Fb l.Definition is_RInt_gen_at_point f a b l :
  is_RInt_gen f (at_point a) (at_point b) l
    <-> is_RInt f a b l.

Lemma is_RInt_gen_plus {Fa Fb : (R -> Prop) -> Prop} {FFa : Filter Fa} {FFb : Filter Fb} (f g : R -> V) (lf lg : V) : is_RInt_gen f Fa Fb lf -> is_RInt_gen g Fa Fb lg -> is_RInt_gen (fun y => plus (f y) (g y)) Fa Fb (plus lf lg).