(*****   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 upd_Znth_app1 {A} i l1 l2 (I: 0 <= i < Zlength l1) (v:A): upd_Znth i (l1++l2) v = upd_Znth i l1 v ++ l2.