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}.