(** ** Continuous imply Riemann-integrable *)
Section StepFun.
Context {V : NormedModule R_AbsRing}.

(* Specifications: *)
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).
Lemma ex_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
ex_RInt (SF_fun (SF_map f s) zero) a b.