intro.simplify.apply le_S_S. apply le_O_n.
intros 2.simplify.elim (nat_compare n1 m1).
simplify. apply le_S_S.apply H.
-simplify. apply le_S_S.apply H.
simplify. apply eq_f. apply H.
+simplify. apply le_S_S.apply H.
qed.
theorem nat_compare_n_m_m_n: \forall n,m:nat.
apply Hcut.apply nat_compare_to_Prop.
elim (nat_compare n m).
apply (H H3).
-apply (H2 H3).
apply (H1 H3).
+apply (H2 H3).
qed.