(*****   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 nth_Znth {A} {d: Inhabitant A}: forall n (xs:list A), 0 <= n < Zlength xs -> (nth (Z.to_nat n) xs d) = (Znth n xs).