src/HOL/Transcendental.thy
 changeset 35038 a1d93ce94235 parent 35028 108662d50512 child 35213 b9866ad4e3be
```--- a/src/HOL/Transcendental.thy	Mon Feb 08 14:06:54 2010 +0100
+++ b/src/HOL/Transcendental.thy	Mon Feb 08 14:06:58 2010 +0100
@@ -2904,10 +2904,12 @@
next
case False hence "0 < \<bar>x\<bar>" and "- \<bar>x\<bar> < \<bar>x\<bar>" by auto
have "suminf (?c (-\<bar>x\<bar>)) - arctan (-\<bar>x\<bar>) = suminf (?c 0) - arctan 0"
-        by (rule suminf_eq_arctan_bounded[where x="0" and a="-\<bar>x\<bar>" and b="\<bar>x\<bar>", symmetric], auto simp add: `\<bar>x\<bar> < r` `-\<bar>x\<bar> < \<bar>x\<bar>`)
+        by (rule suminf_eq_arctan_bounded[where x="0" and a="-\<bar>x\<bar>" and b="\<bar>x\<bar>", symmetric])
+          (simp_all only: `\<bar>x\<bar> < r` `-\<bar>x\<bar> < \<bar>x\<bar>` neg_less_iff_less)
moreover
have "suminf (?c x) - arctan x = suminf (?c (-\<bar>x\<bar>)) - arctan (-\<bar>x\<bar>)"
-        by (rule suminf_eq_arctan_bounded[where x="x" and a="-\<bar>x\<bar>" and b="\<bar>x\<bar>"], auto simp add: `\<bar>x\<bar> < r` `-\<bar>x\<bar> < \<bar>x\<bar>`)
+        by (rule suminf_eq_arctan_bounded[where x="x" and a="-\<bar>x\<bar>" and b="\<bar>x\<bar>"])
+          (simp_all only: `\<bar>x\<bar> < r` `-\<bar>x\<bar> < \<bar>x\<bar>` neg_less_iff_less)
ultimately
show ?thesis using suminf_arctan_zero by auto
qed```