src/HOL/Number_Theory/Euclidean_Algorithm.thy

     hence "Lcm_eucl A = 0" by (auto simp: Lcm_eucl_def)
     with False show ?thesis by auto
   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"])
       apply (rule exI[of _ l\<^sub>0])
       apply (simp add: l\<^sub>0_props)