--- a/src/HOL/Data_Structures/Tree234_Map.thy Tue Jun 12 07:18:18 2018 +0200
+++ b/src/HOL/Data_Structures/Tree234_Map.thy Tue Jun 12 17:18:40 2018 +0200
@@ -123,7 +123,7 @@
by(induction t)
(auto simp: upd_list_simps, auto simp: upd_list_simps split: up\<^sub>i.splits)
-lemma inorder_update:
+lemma inorder_update_234:
"sorted1(inorder t) \<Longrightarrow> inorder(update a b t) = upd_list a b (inorder t)"
by(simp add: update_def inorder_upd)
@@ -133,7 +133,7 @@
(auto simp: del_list_simps inorder_nodes split_minD split!: if_splits prod.splits)
(* 30 secs (2016) *)
-lemma inorder_delete: "\<lbrakk> bal t ; sorted1(inorder t) \<rbrakk> \<Longrightarrow>
+lemma inorder_delete_234: "\<lbrakk> bal t ; sorted1(inorder t) \<rbrakk> \<Longrightarrow>
inorder(delete x t) = del_list x (inorder t)"
by(simp add: delete_def inorder_del)
@@ -161,18 +161,18 @@
subsection \<open>Overall Correctness\<close>
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 = bal
proof (standard, goal_cases)
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_234)
next
- case 4 thus ?case by(simp add: inorder_delete)
+ case 4 thus ?case by(simp add: inorder_delete_234)
next
case 6 thus ?case by(simp add: bal_update)
next
case 7 thus ?case by(simp add: bal_delete)
-qed simp+
+qed (simp add: empty_def)+
end