--- a/src/HOL/Transcendental.thy Mon Mar 16 15:30:00 2015 +0000
+++ b/src/HOL/Transcendental.thy Tue Mar 17 12:23:56 2015 +0000
@@ -16,6 +16,9 @@
lemma real_fact_nat [simp]: "real (fact n :: nat) = fact n"
by (simp add: real_of_nat_def)
+lemma real_fact_int [simp]: "real (fact n :: int) = fact n"
+ by (metis of_int_of_nat_eq of_nat_fact real_of_int_def)
+
lemma root_test_convergence:
fixes f :: "nat \<Rightarrow> 'a::banach"
assumes f: "(\<lambda>n. root n (norm (f n))) ----> x" -- "could be weakened to lim sup"
@@ -4372,7 +4375,6 @@
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"
- thm suminf_eq_arctan_bounded
by (rule suminf_eq_arctan_bounded[where x1="0" and a1="-\<bar>x\<bar>" and b1="\<bar>x\<bar>", symmetric])
(simp_all only: `\<bar>x\<bar> < r` `-\<bar>x\<bar> < \<bar>x\<bar>` neg_less_iff_less)
moreover