proposition: Lemma compare_Lt : forall x y, compare x y = Lt <-> lt x y.
proof: Proof. unfold compare. intros x y; destruct (compare_spec x y); intuition; try discriminate. - rewrite H in H0. elim (StrictOrder_Irreflexive y); auto. - rewrite H in H0. elim (StrictOrder_Irreflexive x); auto. Qed.
imports: OrderedType Orders