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_SF (f : R -> V) (s : SF_seq) : SF_sorted Rle s -> let a := SF_h s in let b := last (SF_h s) (unzip1 (SF_t s)) in is_RInt (SF_fun (SF_map f s) zero) a b (Riemann_sum f s).