(*****   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_list_repeat {A} i j k (v:A) (I: 0<=i) (IJK: i <= j <= k): sublist i j (list_repeat (Z.to_nat k) v) = list_repeat (Z.to_nat (j-i)) v.