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_semantics :
forall (l:alist A) (n:nat),
S n <= length l ->
{y : A | alist_semantics A l (alist_nth_ad n l) = Some y}.