+theorem divides_to_max_prime_factor1 : \forall n,m. O < n \to O < m \to n \divides m \to
+max_prime_factor n \le max_prime_factor m.
+intros 3.
+elim (le_to_or_lt_eq ? ? H)
+ [apply divides_to_max_prime_factor
+ [assumption|assumption|assumption]
+ |rewrite < H1.
+ simplify.apply le_O_n.
+ ]
+qed.
+