Ltac address_ordered_auto :=
      auto; repeat match goal with
                   | H: AddressOrdered.eq ?A ?A |- _ => clear H
                   | H: AddressOrdered.eq ?A ?B |- _ => hnf in H; subst A
                   | H: ?A <> ?A |- _ => contradiction H; reflexivity
                   | H: AddressOrdered.lt ?A ?A |- _ =>
                     apply AddressOrdered.lt_not_eq in H; contradiction H; reflexivity
                   | H: AddressOrdered.lt ?A ?B, H': AddressOrdered.lt ?B ?A |- _ =>
                     contradiction (AddressOrdered.lt_not_eq (AddressOrdered.lt_trans H H')); reflexivity
                   end.

Lemma PX_in_rev: forall elt a m, AMap.Raw.PX.In (elt:=elt) a m <-> AMap.Raw.PX.In a (rev m).