src/HOL/Data_Structures/Tree23_Set.thy
changeset 68431 b294e095f64c
parent 68109 cebf36c14226
child 68440 6826718f732d
     1.1 --- a/src/HOL/Data_Structures/Tree23_Set.thy	Tue Jun 12 07:18:18 2018 +0200
     1.2 +++ b/src/HOL/Data_Structures/Tree23_Set.thy	Tue Jun 12 17:18:40 2018 +0200
     1.3 @@ -11,6 +11,9 @@
     1.4  
     1.5  declare sorted_wrt.simps(2)[simp del]
     1.6  
     1.7 +definition empty :: "'a tree23" where
     1.8 +"empty = Leaf"
     1.9 +
    1.10  fun isin :: "'a::linorder tree23 \<Rightarrow> 'a \<Rightarrow> bool" where
    1.11  "isin Leaf x = False" |
    1.12  "isin (Node2 l a r) x =
    1.13 @@ -377,7 +380,7 @@
    1.14  subsection \<open>Overall Correctness\<close>
    1.15  
    1.16  interpretation Set_by_Ordered
    1.17 -where empty = Leaf and isin = isin and insert = insert and delete = delete
    1.18 +where empty = empty and isin = isin and insert = insert and delete = delete
    1.19  and inorder = inorder and inv = bal
    1.20  proof (standard, goal_cases)
    1.21    case 2 thus ?case by(simp add: isin_set)
    1.22 @@ -389,6 +392,6 @@
    1.23    case 6 thus ?case by(simp add: bal_insert)
    1.24  next
    1.25    case 7 thus ?case by(simp add: bal_delete)
    1.26 -qed simp+
    1.27 +qed (simp add: empty_def)+
    1.28  
    1.29  end