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 norm_RInt_le : forall (f : R -> V) (g : R -> R) (a b : R) (lf : V) (lg : R), a <= b -> (forall x, a <= x <= b -> norm (f x) <= g x) -> is_RInt f a b lf -> is_RInt g a b lg -> norm lf <= lg.