changeset 32877 | 6f09346c7c08 |
parent 32707 | 836ec9d0a0c8 |
child 33271 | 7be66dee1a5a |
--- a/src/HOL/Series.thy Mon Oct 05 16:41:06 2009 +0100 +++ b/src/HOL/Series.thy Mon Oct 05 17:27:46 2009 +0100 @@ -32,6 +32,9 @@ "\<Sum>i. b" == "CONST suminf (%i. b)" +lemma [trans]: "f=g ==> g sums z ==> f sums z" + by simp + lemma sumr_diff_mult_const: "setsum f {0..<n} - (real n*r) = setsum (%i. f i - r) {0..<n::nat}" by (simp add: diff_minus setsum_addf real_of_nat_def)