src/HOL/Data_Structures/Tree234_Map.thy
changeset 68431 b294e095f64c
parent 68020 6aade817bee5
child 68440 6826718f732d
     1.1 --- a/src/HOL/Data_Structures/Tree234_Map.thy	Tue Jun 12 07:18:18 2018 +0200
     1.2 +++ b/src/HOL/Data_Structures/Tree234_Map.thy	Tue Jun 12 17:18:40 2018 +0200
     1.3 @@ -123,7 +123,7 @@
     1.4  by(induction t)
     1.5    (auto simp: upd_list_simps, auto simp: upd_list_simps split: up\<^sub>i.splits)
     1.6  
     1.7 -lemma inorder_update:
     1.8 +lemma inorder_update_234:
     1.9    "sorted1(inorder t) \<Longrightarrow> inorder(update a b t) = upd_list a b (inorder t)"
    1.10  by(simp add: update_def inorder_upd)
    1.11  
    1.12 @@ -133,7 +133,7 @@
    1.13    (auto simp: del_list_simps inorder_nodes split_minD split!: if_splits prod.splits)
    1.14  (* 30 secs (2016) *)
    1.15  
    1.16 -lemma inorder_delete: "\<lbrakk> bal t ; sorted1(inorder t) \<rbrakk> \<Longrightarrow>
    1.17 +lemma inorder_delete_234: "\<lbrakk> bal t ; sorted1(inorder t) \<rbrakk> \<Longrightarrow>
    1.18    inorder(delete x t) = del_list x (inorder t)"
    1.19  by(simp add: delete_def inorder_del)
    1.20  
    1.21 @@ -161,18 +161,18 @@
    1.22  subsection \<open>Overall Correctness\<close>
    1.23  
    1.24  interpretation Map_by_Ordered
    1.25 -where empty = Leaf and lookup = lookup and update = update and delete = delete
    1.26 +where empty = empty and lookup = lookup and update = update and delete = delete
    1.27  and inorder = inorder and inv = bal
    1.28  proof (standard, goal_cases)
    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_234)
    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_234)
    1.36  next
    1.37    case 6 thus ?case by(simp add: bal_update)
    1.38  next
    1.39    case 7 thus ?case by(simp add: bal_delete)
    1.40 -qed simp+
    1.41 +qed (simp add: empty_def)+
    1.42  
    1.43  end