--- a/src/HOL/ex/Sqrt.thy Sat Jul 05 10:09:01 2014 +0200
+++ b/src/HOL/ex/Sqrt.thy Sat Jul 05 11:01:53 2014 +0200
@@ -33,7 +33,7 @@
from eq have "p dvd m\<^sup>2" ..
with `prime p` show "p dvd m" by (rule prime_dvd_power_nat)
then obtain k where "m = p * k" ..
- with eq have "p * n\<^sup>2 = p\<^sup>2 * k\<^sup>2" by (auto simp add: power2_eq_square mult_ac)
+ with eq have "p * n\<^sup>2 = p\<^sup>2 * k\<^sup>2" by (auto simp add: power2_eq_square ac_simps)
with p have "n\<^sup>2 = p * k\<^sup>2" by (simp add: power2_eq_square)
then have "p dvd n\<^sup>2" ..
with `prime p` show "p dvd n" by (rule prime_dvd_power_nat)
@@ -73,7 +73,7 @@
then have "p dvd m\<^sup>2" ..
with `prime p` have dvd_m: "p dvd m" by (rule prime_dvd_power_nat)
then obtain k where "m = p * k" ..
- with eq have "p * n\<^sup>2 = p\<^sup>2 * k\<^sup>2" by (auto simp add: power2_eq_square mult_ac)
+ with eq have "p * n\<^sup>2 = p\<^sup>2 * k\<^sup>2" by (auto simp add: power2_eq_square ac_simps)
with p have "n\<^sup>2 = p * k\<^sup>2" by (simp add: power2_eq_square)
then have "p dvd n\<^sup>2" ..
with `prime p` have "p dvd n" by (rule prime_dvd_power_nat)