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').