Definition RInt_gen (f : R -> V) (a b : (R -> Prop) -> Prop) :=
  iota (is_RInt_gen f a b).

Lemma is_RInt_gen_Derive {Fa Fb : (R -> Prop) -> Prop} {FFa : Filter Fa} {FFb : Filter Fb} (f : R -> R) (la lb : R) : filter_prod Fa Fb (fun ab => forall x : R, Rmin (fst ab) (snd ab) <= x <= Rmax (fst ab) (snd ab) -> ex_derive f x) -> filter_prod Fa Fb (fun ab => forall x : R, Rmin (fst ab) (snd ab) <= x <= Rmax (fst ab) (snd ab) -> continuous (Derive f) x) -> filterlim f Fa (locally la) -> filterlim f Fb (locally lb) -> is_RInt_gen (Derive f) Fa Fb (lb - la).