--- a/src/HOL/Data_Structures/AA_Set.thy Tue Jun 12 07:18:18 2018 +0200
+++ b/src/HOL/Data_Structures/AA_Set.thy Tue Jun 12 17:18:40 2018 +0200
@@ -12,6 +12,9 @@
type_synonym 'a aa_tree = "('a,nat) tree"
+definition empty :: "'a aa_tree" where
+"empty = Leaf"
+
fun lvl :: "'a aa_tree \<Rightarrow> nat" where
"lvl Leaf = 0" |
"lvl (Node _ _ lv _) = lv"
@@ -483,10 +486,10 @@
post_split_max post_delete split_maxD split: prod.splits)
interpretation I: 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 = invar
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_inorder)
next
@@ -494,7 +497,7 @@
next
case 4 thus ?case by(simp add: inorder_delete)
next
- case 5 thus ?case by(simp)
+ case 5 thus ?case by(simp add: empty_def)
next
case 6 thus ?case by(simp add: invar_insert)
next