(*****   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_rejoin': forall {A} lo mid mid' hi (al: list A), mid=mid' -> 0 <= lo <= mid -> mid' <= hi <= Zlength al -> sublist lo mid al ++ sublist mid' hi al = sublist lo hi al.