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_nth_ad_aapp_1 :
forall (l l':alist A) (n:nat),
S n <= length l -> alist_nth_ad n (aapp A l l') = alist_nth_ad n l.