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