(*****   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 upd_Znth_lookup' K {A}{d: Inhabitant A}: forall l (L:Zlength l = K) i (I: 0<=i<K) j (J: 0<=j<K) (v:A), Znth i (upd_Znth j l v) = if zeq i j then v else Znth i l.