proposition: Lemma ltM_equiv_ltMR : forall a l l' l'', ltM a l l' -> equiv l l'' -> ltM a l'' l'.
proof: Proof. unfold ltM, equiv. intros. case H; intros; clear H. split. rewrite <- H0; auto. intros; rewrite <- H0;auto. Qed.
imports: Arith Omega ArithRing More_nat EPSILON0