Section RInt_gen.
Context {V : CompleteNormedModule R_AbsRing}.
Definition RInt_gen (f : R -> V) (a b : (R -> Prop) -> Prop) :=
iota (is_RInt_gen f a b).

Lemma RInt_gen_ext {Fa Fb : (R -> Prop) -> Prop}
{FFa : ProperFilter Fa} {FFb : ProperFilter Fb} (f g : R -> V) :
filter_prod Fa Fb (fun ab => forall x, Rmin (fst ab) (snd ab) < x < Rmax (fst ab) (snd ab)
-> f x = g x) ->
ex_RInt_gen f Fa Fb -> RInt_gen f Fa Fb = RInt_gen g Fa Fb.