src/HOL/Big_Operators.thy
changeset 54230 b1d955791529
parent 54147 97a8ff4e4ac9
child 54555 e8c5e95d338b
--- a/src/HOL/Big_Operators.thy	Thu Oct 31 16:54:22 2013 +0100
+++ b/src/HOL/Big_Operators.thy	Fri Nov 01 18:51:14 2013 +0100
@@ -696,11 +696,7 @@
 lemma setsum_subtractf:
   "setsum (%x. ((f x)::'a::ab_group_add) - g x) A =
     setsum f A - setsum g A"
-proof (cases "finite A")
-  case True thus ?thesis by (simp add: diff_minus setsum_addf setsum_negf)
-next
-  case False thus ?thesis by simp
-qed
+  using setsum_addf [of f "- g" A] by (simp add: setsum_negf)
 
 lemma setsum_nonneg:
   assumes nn: "\<forall>x\<in>A. (0::'a::{ordered_ab_semigroup_add,comm_monoid_add}) \<le> f x"