--- a/src/HOL/Data_Structures/Tree_Map.thy Tue Jun 12 07:18:18 2018 +0200
+++ b/src/HOL/Data_Structures/Tree_Map.thy Tue Jun 12 17:18:40 2018 +0200
@@ -34,25 +34,25 @@
"sorted1(inorder t) \<Longrightarrow> lookup t x = map_of (inorder t) x"
by (induction t) (auto simp: map_of_simps split: option.split)
-lemma inorder_update:
+lemma inorder_update_tree:
"sorted1(inorder t) \<Longrightarrow> inorder(update a b t) = upd_list a b (inorder t)"
by(induction t) (auto simp: upd_list_simps)
-lemma inorder_delete:
+lemma inorder_delete_tree:
"sorted1(inorder t) \<Longrightarrow> inorder(delete x t) = del_list x (inorder t)"
by(induction t) (auto simp: del_list_simps split_minD split: prod.splits)
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 = "\<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: lookup_map_of)
next
- case 3 thus ?case by(simp add: inorder_update)
+ case 3 thus ?case by(simp add: inorder_update_tree)
next
- case 4 thus ?case by(simp add: inorder_delete)
+ case 4 thus ?case by(simp add: inorder_delete_tree)
qed auto
end