src/HOL/Transcendental.thy
 changeset 59647 c6f413b660cf parent 59613 7103019278f0 child 59658 0cc388370041
```     1.1 --- a/src/HOL/Transcendental.thy	Sat Mar 07 15:40:36 2015 +0100
1.2 +++ b/src/HOL/Transcendental.thy	Sat Mar 07 21:32:31 2015 +0100
1.3 @@ -4028,11 +4028,12 @@
1.4          case False
1.5          hence "0 < \<bar>x\<bar>" and "- \<bar>x\<bar> < \<bar>x\<bar>" by auto
1.6          have "suminf (?c (-\<bar>x\<bar>)) - arctan (-\<bar>x\<bar>) = suminf (?c 0) - arctan 0"
1.7 -          by (rule suminf_eq_arctan_bounded[where x="0" and a="-\<bar>x\<bar>" and b="\<bar>x\<bar>", symmetric])
1.8 +        thm suminf_eq_arctan_bounded
1.9 +          by (rule suminf_eq_arctan_bounded[where x1="0" and a1="-\<bar>x\<bar>" and b1="\<bar>x\<bar>", symmetric])
1.10              (simp_all only: `\<bar>x\<bar> < r` `-\<bar>x\<bar> < \<bar>x\<bar>` neg_less_iff_less)
1.11          moreover
1.12          have "suminf (?c x) - arctan x = suminf (?c (-\<bar>x\<bar>)) - arctan (-\<bar>x\<bar>)"
1.13 -          by (rule suminf_eq_arctan_bounded[where x="x" and a="-\<bar>x\<bar>" and b="\<bar>x\<bar>"])
1.14 +          by (rule suminf_eq_arctan_bounded[where x1="x" and a1="-\<bar>x\<bar>" and b1="\<bar>x\<bar>"])
1.15               (simp_all only: `\<bar>x\<bar> < r` `-\<bar>x\<bar> < \<bar>x\<bar>` neg_less_iff_less)
1.16          ultimately
1.17          show ?thesis using suminf_arctan_zero by auto
```