Definition min_elt m : option (key*elt) := match elements m with
| nil => None
| (x,e)::_ => Some (x,e)
end.

(* Specifications: *)
Lemma min_elt_Below :
forall m x e, min_elt m = Some (x,e) -> Below x (remove x m).
Lemma min_elt_MapsTo :
forall m x e, min_elt m = Some (x,e) -> MapsTo x e m.
Lemma min_elt_Empty :
forall m, min_elt m = None -> Empty m.