proposition: Lemma compare_spec : forall s1 s2 `{Ok s1, Ok s2}, CompSpec eq lt s1 s2 (compare s1 s2).
proof: Proof. intros. destruct (compare_Cmp s1 s2); constructor. - rewrite eq_Leq; auto. - intros; exists s1, s2; repeat split; auto. - intros; exists s2, s1; repeat split; auto. Qed.
imports: Orders OrdersFacts MSetInterface PeanoNat