# HG changeset patch
# User huffman
# Date 1323434536 -3600
# Node ID 16e8e4d33c426d5753459e8ec9dbf3b448b87b5e
# Parent  331ebffe0593a3210cfcbbcc93977bd7c45a1ef0
add induction rule for list_all2

diff -r 331ebffe0593 -r 16e8e4d33c42 src/HOL/List.thy
--- a/src/HOL/List.thy	Fri Dec 09 12:21:03 2011 +0100
+++ b/src/HOL/List.thy	Fri Dec 09 13:42:16 2011 +0100
@@ -2202,6 +2202,15 @@
 "list_all2 P xs (y # ys) = (\<exists>z zs. xs = z # zs \<and> P z y \<and> list_all2 P zs ys)"
 by (cases xs) auto
 
+lemma list_all2_induct
+  [consumes 1, case_names Nil Cons, induct set: list_all2]:
+  assumes P: "list_all2 P xs ys"
+  assumes Nil: "R [] []"
+  assumes Cons: "\<And>x xs y ys. \<lbrakk>P x y; R xs ys\<rbrakk> \<Longrightarrow> R (x # xs) (y # ys)"
+  shows "R xs ys"
+using P
+by (induct xs arbitrary: ys) (auto simp add: list_all2_Cons1 Nil Cons)
+
 lemma list_all2_rev [iff]:
 "list_all2 P (rev xs) (rev ys) = list_all2 P xs ys"
 by (simp add: list_all2_def zip_rev cong: conj_cong)