--- a/src/HOL/SPARK/Examples/Sqrt/Sqrt.thy Thu May 26 16:57:14 2016 +0200
+++ b/src/HOL/SPARK/Examples/Sqrt/Sqrt.thy Thu May 26 17:51:22 2016 +0200
@@ -11,13 +11,13 @@
spark_vc function_isqrt_4
proof -
- from `0 \<le> r` have "(r = 0 \<or> r = 1 \<or> r = 2) \<or> 2 < r" by auto
+ from \<open>0 \<le> r\<close> have "(r = 0 \<or> r = 1 \<or> r = 2) \<or> 2 < r" by auto
then show "2 * r \<le> 2147483646"
proof
assume "2 < r"
then have "0 < r" by simp
- with `2 < r` have "2 * r < r * r" by (rule mult_strict_right_mono)
- with `r * r \<le> n` and `n \<le> 2147483647` show ?thesis
+ with \<open>2 < r\<close> have "2 * r < r * r" by (rule mult_strict_right_mono)
+ with \<open>r * r \<le> n\<close> and \<open>n \<le> 2147483647\<close> show ?thesis
by simp
qed auto
then show "2 * r \<le> 2147483647" by simp