(** SF_sup and SF_inf *)
Definition SF_sup_seq (f : R -> R) (a b : R) (n : nat) : SF_seq :=
SF_seq_f2 (Sup_fct f) (unif_part a b n).

Lemma SF_sup_ly (f : R -> R) (a b : R) (n : nat) :
SF_ly (SF_sup_seq f a b n) = behead (pairmap (Sup_fct f) 0 (unif_part a b n)).