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 alist_sorted_1_imp_2 : forall l:alist A, alist_sorted_1 l -> alist_sorted_2 l.