--- a/src/HOL/Number_Theory/Euclidean_Algorithm.thy Sun Apr 24 21:31:14 2016 +0200
+++ b/src/HOL/Number_Theory/Euclidean_Algorithm.thy Mon Apr 25 16:09:26 2016 +0200
@@ -159,8 +159,8 @@
next
case True
then obtain l\<^sub>0 where l\<^sub>0_props: "l\<^sub>0 \<noteq> 0 \<and> (\<forall>a\<in>A. a dvd l\<^sub>0)" by blast
- def n \<equiv> "LEAST n. \<exists>l. l \<noteq> 0 \<and> (\<forall>a\<in>A. a dvd l) \<and> euclidean_size l = n"
- def l \<equiv> "SOME l. l \<noteq> 0 \<and> (\<forall>a\<in>A. a dvd l) \<and> euclidean_size l = n"
+ define n where "n = (LEAST n. \<exists>l. l \<noteq> 0 \<and> (\<forall>a\<in>A. a dvd l) \<and> euclidean_size l = n)"
+ define l where "l = (SOME l. l \<noteq> 0 \<and> (\<forall>a\<in>A. a dvd l) \<and> euclidean_size l = n)"
have "\<exists>l. l \<noteq> 0 \<and> (\<forall>a\<in>A. a dvd l) \<and> euclidean_size l = n"
apply (subst n_def)
apply (rule LeastI[of _ "euclidean_size l\<^sub>0"])