--- a/src/HOL/Data_Structures/AVL_Map.thy Tue Jun 12 07:18:18 2018 +0200
+++ b/src/HOL/Data_Structures/AVL_Map.thy Tue Jun 12 17:18:40 2018 +0200
@@ -25,12 +25,12 @@
subsection \<open>Functional Correctness\<close>
-theorem inorder_update:
+theorem inorder_update_avl:
"sorted1(inorder t) \<Longrightarrow> inorder(update x y t) = upd_list x y (inorder t)"
by (induct t) (auto simp: upd_list_simps inorder_balL inorder_balR)
-theorem inorder_delete:
+theorem inorder_delete_avl:
"sorted1(inorder t) \<Longrightarrow> inorder (delete x t) = del_list x (inorder t)"
by(induction t)
(auto simp: del_list_simps inorder_balL inorder_balR
@@ -181,18 +181,18 @@
interpretation Map_by_Ordered
-where empty = Leaf and lookup = lookup and update = update and delete = delete
+where empty = empty and lookup = lookup and update = update and delete = delete
and inorder = inorder and inv = avl
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: lookup_map_of)
next
- case 3 thus ?case by(simp add: inorder_update)
+ case 3 thus ?case by(simp add: inorder_update_avl)
next
- case 4 thus ?case by(simp add: inorder_delete)
+ case 4 thus ?case by(simp add: inorder_delete_avl)
next
- case 5 show ?case by simp
+ case 5 show ?case by (simp add: empty_def)
next
case 6 thus ?case by(simp add: avl_update(1))
next