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 interval_split : forall p q n:nat, S n <= p + q -> {n' : nat | S n' <= q /\ n = p + n'} + {S n <= p}.