Definition is_RInt (f : R -> V) (a b : R) (If : V) :=
  filterlim (fun ptd => scal (sign (b-a)) (Riemann_sum f ptd)) (Riemann_fine a b) (locally If).Definition ex_RInt (f : R -> V) (a b : R) :=
  exists If : V, is_RInt f a b If.

Lemma is_RInt_Chasles_1 (f : R -> V) (a b c : R) l1 l2 : a < b < c -> is_RInt f a c l1 -> is_RInt f b c l2 -> is_RInt f a b (minus l1 l2).