(** The dependent-style [compare] *)
Definition eq (m1 m2 : t) := LO.eq_list (elements m1) (elements m2).
Definition lt (m1 m2 : t) := LO.lt_list (elements m1) (elements m2).
Definition compare (s s':t) : Compare lt eq s s'.

Lemma lt_trans : forall m1 m2 m3 : t, lt m1 m2 -> lt m2 m3 -> lt m1 m3.