src/HOL/Data_Structures/Tree_Map.thy
changeset 68431 b294e095f64c
parent 68020 6aade817bee5
child 68440 6826718f732d
     1.1 --- a/src/HOL/Data_Structures/Tree_Map.thy	Tue Jun 12 07:18:18 2018 +0200
     1.2 +++ b/src/HOL/Data_Structures/Tree_Map.thy	Tue Jun 12 17:18:40 2018 +0200
     1.3 @@ -34,25 +34,25 @@
     1.4    "sorted1(inorder t) \<Longrightarrow> lookup t x = map_of (inorder t) x"
     1.5  by (induction t) (auto simp: map_of_simps split: option.split)
     1.6  
     1.7 -lemma inorder_update:
     1.8 +lemma inorder_update_tree:
     1.9    "sorted1(inorder t) \<Longrightarrow> inorder(update a b t) = upd_list a b (inorder t)"
    1.10  by(induction t) (auto simp: upd_list_simps)
    1.11  
    1.12 -lemma inorder_delete:
    1.13 +lemma inorder_delete_tree:
    1.14    "sorted1(inorder t) \<Longrightarrow> inorder(delete x t) = del_list x (inorder t)"
    1.15  by(induction t) (auto simp: del_list_simps split_minD split: prod.splits)
    1.16  
    1.17  interpretation Map_by_Ordered
    1.18 -where empty = Leaf and lookup = lookup and update = update and delete = delete
    1.19 +where empty = empty and lookup = lookup and update = update and delete = delete
    1.20  and inorder = inorder and inv = "\<lambda>_. True"
    1.21  proof (standard, goal_cases)
    1.22 -  case 1 show ?case by simp
    1.23 +  case 1 show ?case by (simp add: empty_def)
    1.24  next
    1.25    case 2 thus ?case by(simp add: lookup_map_of)
    1.26  next
    1.27 -  case 3 thus ?case by(simp add: inorder_update)
    1.28 +  case 3 thus ?case by(simp add: inorder_update_tree)
    1.29  next
    1.30 -  case 4 thus ?case by(simp add: inorder_delete)
    1.31 +  case 4 thus ?case by(simp add: inorder_delete_tree)
    1.32  qed auto
    1.33  
    1.34  end