--- a/src/HOL/Data_Structures/Tree_Set.thy Tue Jun 12 07:18:18 2018 +0200
+++ b/src/HOL/Data_Structures/Tree_Set.thy Tue Jun 12 17:18:40 2018 +0200
@@ -9,6 +9,9 @@
Set_Specs
begin
+definition empty :: "'a tree" where
+"empty == Leaf"
+
fun isin :: "'a::linorder tree \<Rightarrow> 'a \<Rightarrow> bool" where
"isin Leaf x = False" |
"isin (Node l a r) x =
@@ -60,10 +63,10 @@
by(induction t) (auto simp: del_list_simps split_minD split: prod.splits)
interpretation Set_by_Ordered
-where empty = Leaf and isin = isin and insert = insert and delete = delete
+where empty = empty and isin = isin and insert = insert and delete = delete
and inorder = inorder and inv = "\<lambda>_. True"
proof (standard, goal_cases)
- case 1 show ?case by simp
+ case 1 show ?case by (simp add: empty_def)
next
case 2 thus ?case by(simp add: isin_set)
next