End SF_map.
(** * Pointed subvivision *)
Definition pointed_subdiv (ptd : @SF_seq R) :=
forall i : nat, (i < SF_size ptd)%nat ->
nth 0 (SF_lx ptd) i <= nth 0 (SF_ly ptd) i <= nth 0 (SF_lx ptd) (S i).

Lemma ptd_sort ptd :
pointed_subdiv ptd -> SF_sorted Rle ptd.