Definition SF_compat_le (s : @SF_seq R) (pr : SF_sorted Rle s) :
StepFun (head 0 (SF_lx s)) (last 0 (SF_lx s)).
(** Build StepFun using uniform partition *)

Lemma ad_SF_val_fun (f : R -> R) (a b : R) (n : nat) :
((a <= b) -> adapted_couple (SF_val_fun f a b n) a b
(seq2Rlist (unif_part a b n)) (seq2Rlist (SF_val_ly f a b n)))
/\ (~(a <= b) -> adapted_couple (SF_val_fun f b a n) a b
(seq2Rlist (unif_part b a n)) (seq2Rlist (SF_val_ly f b a n))).