(*****   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_upd_Znth_lr: forall {A} (l: list A) i lo hi v, 0 <= lo <= i-> i < hi <= Zlength l -> sublist lo hi (upd_Znth i l v) = upd_Znth (i - lo) (sublist lo hi l) v.