--- a/NEWS Mon May 10 15:33:32 2010 +0200
+++ b/NEWS Tue May 11 08:29:42 2010 +0200
@@ -140,6 +140,9 @@
*** HOL ***
+* Theorem Presburger.int_induct has been renamed to Int.int_bidirectional_induct;
+theorem Int.int_induct is no longer shadowed. INCOMPATIBILITY.
+
* Dropped theorem duplicate comp_arith; use semiring_norm instead. INCOMPATIBILITY.
* Theory 'Finite_Set': various folding_* locales facilitate the application
--- a/src/HOL/Library/Formal_Power_Series.thy Mon May 10 15:33:32 2010 +0200
+++ b/src/HOL/Library/Formal_Power_Series.thy Tue May 11 08:29:42 2010 +0200
@@ -402,7 +402,7 @@
lemma number_of_fps_const: "(number_of k::('a::comm_ring_1) fps) = fps_const (of_int k)"
-proof(induct k rule: int_induct[where k=0])
+proof(induct k rule: int_bidirectional_induct [where k=0])
case base thus ?case unfolding number_of_fps_def of_int_0 by simp
next
case (step1 i) thus ?case unfolding number_of_fps_def
@@ -3214,7 +3214,7 @@
lemma fps_number_of_fps_const: "number_of i = fps_const (number_of i :: 'a:: {comm_ring_1, number_ring})"
apply (subst (2) number_of_eq)
-apply(rule int_induct[of _ 0])
+apply(rule int_bidirectional_induct[of _ 0])
apply (simp_all add: number_of_fps_def)
by (simp_all add: fps_const_add[symmetric] fps_const_minus[symmetric])
--- a/src/HOL/ex/Summation.thy Mon May 10 15:33:32 2010 +0200
+++ b/src/HOL/ex/Summation.thy Tue May 11 08:29:42 2010 +0200
@@ -42,7 +42,7 @@
proof -
fix k
show "f k - g k = f 0 - g 0"
- by (induct k rule: int_induct) (simp_all add: k_incr k_decr)
+ by (induct k rule: int_bidirectional_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)