Definition ad_monotonic (pf:ad -> ad) :=
    forall a a':ad, Nless a a' = true -> Nless (pf a) (pf a') = true.

Lemma alist_sorted_tail : forall (l:alist A) (a:ad) (y:A), alist_sorted_2 ((a, y) :: l) -> alist_sorted_2 l.