src/HOL/Data_Structures/Tree_Set.thy
changeset 68431 b294e095f64c
parent 68020 6aade817bee5
child 68440 6826718f732d
     1.1 --- a/src/HOL/Data_Structures/Tree_Set.thy	Tue Jun 12 07:18:18 2018 +0200
     1.2 +++ b/src/HOL/Data_Structures/Tree_Set.thy	Tue Jun 12 17:18:40 2018 +0200
     1.3 @@ -9,6 +9,9 @@
     1.4    Set_Specs
     1.5  begin
     1.6  
     1.7 +definition empty :: "'a tree" where
     1.8 +"empty == Leaf"
     1.9 +
    1.10  fun isin :: "'a::linorder tree \<Rightarrow> 'a \<Rightarrow> bool" where
    1.11  "isin Leaf x = False" |
    1.12  "isin (Node l a r) x =
    1.13 @@ -60,10 +63,10 @@
    1.14  by(induction t) (auto simp: del_list_simps split_minD split: prod.splits)
    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 = "\<lambda>_. True"
    1.20  proof (standard, goal_cases)
    1.21 -  case 1 show ?case by simp
    1.22 +  case 1 show ?case by (simp add: empty_def)
    1.23  next
    1.24    case 2 thus ?case by(simp add: isin_set)
    1.25  next