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

Lemma alist_of_Map_sorts_1 : forall (m:Map A) (pf:ad -> ad), ad_monotonic pf -> alist_sorted_2 (MapFold1 A (alist A) (anil A) (aapp A) (fun (a:ad) (y:A) => acons A (a, y) (anil A)) pf m).