Definition SF_sup_r (f : R -> R) (a b : R) (n : nat) : StepFun a b.

(* Specifications: *)
Lemma SF_sup_subdiv_val (f : R -> R) (a b : R) (n : nat) :
subdivision_val (SF_sup_r f a b n) =
match (Rle_dec a b) with
| left _ => (seq2Rlist (behead (pairmap (fun x y => real (Sup_fct f x y)) 0 (unif_part a b n))))
| right _ => (seq2Rlist (behead (pairmap (fun x y => real (Sup_fct f x y)) 0 (unif_part b a n))))
end.
Lemma SF_sup_r_bound (f : R -> R) (a b : R) (n : nat) :
forall x, SF_sup_r f a b n x = SF_sup_r f b a n x.