--- a/src/HOL/Complex/ex/MIR.thy Wed Jul 25 22:20:54 2007 +0200
+++ b/src/HOL/Complex/ex/MIR.thy Thu Jul 26 21:48:01 2007 +0200
@@ -2140,17 +2140,17 @@
let ?d = "\<delta> (And p q)"
from prems ilcm_pos have dp: "?d >0" by simp
have d1: "\<delta> p dvd \<delta> (And p q)" using prems ilcm_dvd1 by simp
- hence th: "d\<delta> p ?d" using delta_mono prems by auto
- have "\<delta> q dvd \<delta> (And p q)" using prems ilcm_dvd2 by simp
- hence th': "d\<delta> q ?d" using delta_mono prems by auto
- from th th' dp show ?case by simp
+ hence th: "d\<delta> p ?d" using delta_mono prems by(auto simp del: dvd_ilcm_self1)
+ have "\<delta> q dvd \<delta> (And p q)" using prems ilcm_dvd2 by(simp)
+ hence th': "d\<delta> q ?d" using delta_mono prems by(auto simp del: dvd_ilcm_self2)
+ from th th' dp show ?case by simp
next
case (2 p q)
let ?d = "\<delta> (And p q)"
from prems ilcm_pos have dp: "?d >0" by simp
- have "\<delta> p dvd \<delta> (And p q)" using prems ilcm_dvd1 by simp hence th: "d\<delta> p ?d" using delta_mono prems by auto
- have "\<delta> q dvd \<delta> (And p q)" using prems ilcm_dvd2 by simp hence th': "d\<delta> q ?d" using delta_mono prems by auto
- from th th' dp show ?case by simp
+ have "\<delta> p dvd \<delta> (And p q)" using prems ilcm_dvd1 by simp hence th: "d\<delta> p ?d" using delta_mono prems by(auto simp del: dvd_ilcm_self1)
+ have "\<delta> q dvd \<delta> (And p q)" using prems ilcm_dvd2 by simp hence th': "d\<delta> q ?d" using delta_mono prems by(auto simp del: dvd_ilcm_self2)
+ from th th' dp show ?case by simp
qed simp_all