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

Lemma RInt_gen_ext_eq {Fa Fb : (R -> Prop) -> Prop} {FFa : ProperFilter Fa} {FFb : ProperFilter Fb} (f g : R -> V): (forall x, f x = g x) -> ex_RInt_gen f Fa Fb -> RInt_gen f Fa Fb = RInt_gen g Fa Fb.