(*****   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_app1: forall (A : Type) (k i : Z) (al bl : list A), 0 <= k <= i -> i <= Zlength al -> sublist k i (al ++ bl) = sublist k i al.