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_sorted_2_imp :
forall l:alist A, alist_sorted_2 l -> alist_sorted l = true.