theorem le_gen_S_S_2: \forall m,n. (le (S m) (S n)) \to (le m n).
intros.
lapply le_gen_S_x_2 to H using H0. elim H0. elim H1.
-lapply eq_gen_S_S to H2 using H4. rewrite left H4. assumption.
+lapply eq_gen_S_S to H2 using H4. rewrite > H4. assumption.
qed.