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

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.