(*****   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 Zlength_sublist_correct: forall {A} (l: list A) (lo hi: Z), 0 <= lo <= hi -> hi <= Zlength l -> Zlength (sublist lo hi l) = hi - lo.