+theorem antisymmetric_divides: antisymmetric nat divides.
+unfold antisymmetric.intros.elim H. elim H1.
+apply (nat_case1 n2).intro.
+rewrite > H3.rewrite > H2.rewrite > H4.
+rewrite < times_n_O.reflexivity.
+intros.
+apply (nat_case1 n).intro.
+rewrite > H2.rewrite > H3.rewrite > H5.
+rewrite < times_n_O.reflexivity.
+intros.
+apply antisymmetric_le.
+rewrite > H2.rewrite > times_n_SO in \vdash (? % ?).
+apply le_times_r.rewrite > H4.apply le_S_S.apply le_O_n.
+rewrite > H3.rewrite > times_n_SO in \vdash (? % ?).
+apply le_times_r.rewrite > H5.apply le_S_S.apply le_O_n.
+qed.
+