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

Lemma RInt_gen_correct {Fa Fb : (R -> Prop) -> Prop} {FFa : ProperFilter' Fa} {FFb : ProperFilter' Fb} (f : R -> V) : ex_RInt_gen f Fa Fb -> is_RInt_gen f Fa Fb (RInt_gen f Fa Fb).