(*****   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_app2 {A} i j (al bl:list A): 0<=Zlength al <= i-> sublist i j (al ++ bl) = sublist (i-Zlength al) (j-Zlength al) bl.