Definition alist_sorted_2 (l:alist A) :=
    forall m n:nat,
      m < n ->
      S n <= length l -> Nless (alist_nth_ad m l) (alist_nth_ad n l) = true.

Lemma app_length : forall (C:Type) (l l':list C), length (l ++ l') = length l + length l'.