(*****   SUBLIST  ******)

Definition sublist {A} (lo hi: Z) (al: list A) : list A :=
  firstn (Z.to_nat (hi-lo)) (skipn (Z.to_nat lo) al).Definition upd_Znth {A} (i: Z) (al: list A) (x: A): list A :=
   sublist 0 i al ++ x :: sublist (i+1) (Zlength al) al.

Lemma sublist_app: forall {A} lo hi (al bl: list A), 0 <= lo <= hi -> hi <= Zlength al + Zlength bl -> sublist lo hi (al++bl) = sublist (Z.min lo (Zlength al)) (Z.min hi (Zlength al)) al ++ sublist (Z.max (lo-Zlength al) 0) (Z.max (hi-Zlength al) 0) bl.