include "datatypes/constructors.ma".
include "nat/exp.ma".
include "nat/gcd.ma".
+include "nat/relevant_equations.ma". (* required by auto paramod *)
(* this definition of log is based on pairs, with a remainder *)
apply le_times_l.
assumption.
apply le_times_r.assumption.
- alias id "not_eq_to_le_to_lt" = "cic:/matita/algebra/finite_groups/not_eq_to_le_to_lt.con".
+alias id "not_eq_to_le_to_lt" = "cic:/matita/algebra/finite_groups/not_eq_to_le_to_lt.con".
apply not_eq_to_le_to_lt.
unfold.intro.apply H1.
rewrite < H3.
elim (divides_times_to_divides ? ? ? H H9).
apply (absurd ? ? H10 H5).
apply (absurd ? ? H10 H7).
-rewrite > H6.
-rewrite > H8.
-auto paramodulation.
+(* rewrite > H6.
+rewrite > H8. *)
+auto paramodulation library=yes.
unfold prime in H. elim H. assumption.
qed.