(*****   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 Znth_sublist:
forall {A}{d: Inhabitant A} lo i hi (al: list A),
0 <= lo ->
0 <= i < hi-lo ->
Znth i (sublist lo hi al) = Znth (i+lo) al.