--- a/src/HOL/Library/Permutation.thy Fri Nov 06 13:42:29 2009 +0100
+++ b/src/HOL/Library/Permutation.thy Sat Nov 07 08:17:52 2009 +0100
@@ -93,11 +93,9 @@
subsection {* Removing elements *}
-consts
- remove :: "'a => 'a list => 'a list"
-primrec
- "remove x [] = []"
- "remove x (y # ys) = (if x = y then ys else y # remove x ys)"
+primrec remove :: "'a => 'a list => 'a list" where
+ "remove x [] = []"
+ | "remove x (y # ys) = (if x = y then ys else y # remove x ys)"
lemma perm_remove: "x \<in> set ys ==> ys <~~> x # remove x ys"
by (induct ys) auto
@@ -156,7 +154,7 @@
done
lemma multiset_of_le_perm_append:
- "(multiset_of xs \<le># multiset_of ys) = (\<exists>zs. xs @ zs <~~> ys)";
+ "(multiset_of xs \<le># multiset_of ys) = (\<exists>zs. xs @ zs <~~> ys)"
apply (auto simp: multiset_of_eq_perm[THEN sym] mset_le_exists_conv)
apply (insert surj_multiset_of, drule surjD)
apply (blast intro: sym)+