src/HOL/Data_Structures/AVL_Map.thy
changeset 68431 b294e095f64c
parent 68422 0a3a36fa1d63
child 68440 6826718f732d
     1.1 --- a/src/HOL/Data_Structures/AVL_Map.thy	Tue Jun 12 07:18:18 2018 +0200
     1.2 +++ b/src/HOL/Data_Structures/AVL_Map.thy	Tue Jun 12 17:18:40 2018 +0200
     1.3 @@ -25,12 +25,12 @@
     1.4  
     1.5  subsection \<open>Functional Correctness\<close>
     1.6  
     1.7 -theorem inorder_update:
     1.8 +theorem inorder_update_avl:
     1.9    "sorted1(inorder t) \<Longrightarrow> inorder(update x y t) = upd_list x y (inorder t)"
    1.10  by (induct t) (auto simp: upd_list_simps inorder_balL inorder_balR)
    1.11  
    1.12  
    1.13 -theorem inorder_delete:
    1.14 +theorem inorder_delete_avl:
    1.15    "sorted1(inorder t) \<Longrightarrow> inorder (delete x t) = del_list x (inorder t)"
    1.16  by(induction t)
    1.17    (auto simp: del_list_simps inorder_balL inorder_balR
    1.18 @@ -181,18 +181,18 @@
    1.19  
    1.20  
    1.21  interpretation Map_by_Ordered
    1.22 -where empty = Leaf and lookup = lookup and update = update and delete = delete
    1.23 +where empty = empty and lookup = lookup and update = update and delete = delete
    1.24  and inorder = inorder and inv = avl
    1.25  proof (standard, goal_cases)
    1.26 -  case 1 show ?case by simp
    1.27 +  case 1 show ?case by (simp add: empty_def)
    1.28  next
    1.29    case 2 thus ?case by(simp add: lookup_map_of)
    1.30  next
    1.31 -  case 3 thus ?case by(simp add: inorder_update)
    1.32 +  case 3 thus ?case by(simp add: inorder_update_avl)
    1.33  next
    1.34 -  case 4 thus ?case by(simp add: inorder_delete)
    1.35 +  case 4 thus ?case by(simp add: inorder_delete_avl)
    1.36  next
    1.37 -  case 5 show ?case by simp
    1.38 +  case 5 show ?case by (simp add: empty_def)
    1.39  next
    1.40    case 6 thus ?case by(simp add: avl_update(1))
    1.41  next