End is_RInt.

(* Specifications: *)
Lemma ex_RInt_Chasles_1 {V : CompleteNormedModule R_AbsRing}
(f : R -> V) (a b c : R) :
a <= b <= c -> ex_RInt f a c -> ex_RInt f a b.
Lemma ex_RInt_Chasles_2 {V : CompleteNormedModule R_AbsRing}
(f : R -> V) (a b c : R) :
a <= b <= c -> ex_RInt f a c -> ex_RInt f b c.
Lemma ex_RInt_inside {V : CompleteNormedModule R_AbsRing} :
forall (f : R -> V) (a b x e : R),
ex_RInt f (x-e) (x+e) -> Rabs (a-x) <= e -> Rabs (b-x) <= e ->
ex_RInt f a b.