diff -r d9a51339746e -r 4ab4aa5bee1c src/HOL/ex/Summation.thy
--- a/src/HOL/ex/Summation.thy	Tue May 11 08:30:02 2010 +0200
+++ b/src/HOL/ex/Summation.thy	Tue May 11 08:36:02 2010 +0200
@@ -42,7 +42,7 @@
   proof -
     fix k
     show "f k - g k = f 0 - g 0"
-      by (induct k rule: int_bidirectional_induct) (simp_all add: k_incr k_decr)
+      by (induct k rule: int_induct) (simp_all add: k_incr k_decr)
   qed
   then have "\<And>k. (plus (g 0 - f 0) \<circ> f) k = g k"
     by (simp add: algebra_simps)