(*****   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_same:
forall {A} lo hi (al: list A),
lo = 0 -> hi = Zlength al ->
sublist lo hi al = al.