author | nipkow |
Tue, 16 Sep 2014 18:42:33 +0200 | |
changeset 58349 | 107341a15946 |
parent 58348 | 2d47c7d10b62 |
child 58350 | 919149921e46 |
--- a/src/HOL/Groups_Big.thy Tue Sep 16 16:04:08 2014 +0200 +++ b/src/HOL/Groups_Big.thy Tue Sep 16 18:42:33 2014 +0200 @@ -948,6 +948,9 @@ apply (auto simp add: algebra_simps) done +lemma setsum_Suc: "setsum (%x. Suc(f x)) A = setsum f A + card A" +using setsum.distrib[of f "%_. 1" A] by(simp) + lemma setsum_bounded: assumes le: "\<And>i. i\<in>A \<Longrightarrow> f i \<le> (K::'a::{semiring_1, ordered_ab_semigroup_add})" shows "setsum f A \<le> of_nat (card A) * K"