changeset 56217 | dc429a5b13c4 |
parent 56213 | e5720d3c18f0 |
child 56369 | 2704ca85be98 |
--- a/src/HOL/Series.thy Wed Mar 19 14:55:47 2014 +0000 +++ b/src/HOL/Series.thy Wed Mar 19 17:06:02 2014 +0000 @@ -461,6 +461,10 @@ apply (auto intro: setsum_mono simp add: abs_less_iff) done +(*A better argument order*) +lemma summable_comparison_test': "summable g \<Longrightarrow> (\<And>n. n \<ge> N \<Longrightarrow> norm(f n) \<le> g n) \<Longrightarrow> summable f" +by (rule summable_comparison_test) auto + subsection {* The Ratio Test*} lemma summable_ratio_test: