--- a/src/HOL/ex/Bubblesort.thy Thu Jun 18 16:17:51 2015 +0200
+++ b/src/HOL/ex/Bubblesort.thy Fri Jun 19 15:55:22 2015 +0200
@@ -41,7 +41,7 @@
by(auto simp: size_bubble_min dest!: bubble_minD_size split: list.splits if_splits)
qed
-lemma mset_bubble_min: "multiset_of (bubble_min xs) = multiset_of xs"
+lemma mset_bubble_min: "mset (bubble_min xs) = mset xs"
apply(induction xs rule: bubble_min.induct)
apply simp
apply simp
@@ -49,19 +49,19 @@
done
lemma bubble_minD_mset:
- "bubble_min (xs) = ys \<Longrightarrow> multiset_of xs = multiset_of ys"
+ "bubble_min (xs) = ys \<Longrightarrow> mset xs = mset ys"
by(auto simp: mset_bubble_min)
lemma mset_bubblesort:
- "multiset_of (bubblesort xs) = multiset_of xs"
+ "mset (bubblesort xs) = mset xs"
apply(induction xs rule: bubblesort.induct)
apply simp
apply simp
by(auto split: list.splits if_splits dest: bubble_minD_mset)
- (metis add_eq_conv_ex mset_bubble_min multiset_of.simps(2))
+ (metis add_eq_conv_ex mset_bubble_min mset.simps(2))
lemma set_bubblesort: "set (bubblesort xs) = set xs"
-by(rule mset_bubblesort[THEN multiset_of_eq_setD])
+by(rule mset_bubblesort[THEN mset_eq_setD])
lemma bubble_min_min: "bubble_min xs = y#ys \<Longrightarrow> z \<in> set ys \<Longrightarrow> y \<le> z"
apply(induction xs arbitrary: y ys z rule: bubble_min.induct)