BT subsumed by Library/Tree

--- a/src/HOL/ROOT	Mon Mar 23 07:36:27 2015 +0100
+++ b/src/HOL/ROOT	Mon Mar 23 08:45:54 2015 +0100
@@ -552,7 +552,6 @@
     Intuitionistic
     CTL
     Arith_Examples
-    BT
     Tree23
     Bubblesort
     MergeSort

--- a/src/HOL/ex/BT.thy	Mon Mar 23 07:36:27 2015 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,160 +0,0 @@
-(*  Title:      HOL/ex/BT.thy
-    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
-    Copyright   1995  University of Cambridge
-
-Binary trees
-*)
-
-section {* Binary trees *}
-
-theory BT imports Main begin
-
-datatype 'a bt =
-    Lf
-  | Br 'a  "'a bt"  "'a bt"
-
-primrec n_nodes :: "'a bt => nat" where
-  "n_nodes Lf = 0"
-| "n_nodes (Br a t1 t2) = Suc (n_nodes t1 + n_nodes t2)"
-
-primrec n_leaves :: "'a bt => nat" where
-  "n_leaves Lf = Suc 0"
-| "n_leaves (Br a t1 t2) = n_leaves t1 + n_leaves t2"
-
-primrec depth :: "'a bt => nat" where
-  "depth Lf = 0"
-| "depth (Br a t1 t2) = Suc (max (depth t1) (depth t2))"
-
-primrec reflect :: "'a bt => 'a bt" where
-  "reflect Lf = Lf"
-| "reflect (Br a t1 t2) = Br a (reflect t2) (reflect t1)"
-
-primrec bt_map :: "('a => 'b) => ('a bt => 'b bt)" where
-  "bt_map f Lf = Lf"
-| "bt_map f (Br a t1 t2) = Br (f a) (bt_map f t1) (bt_map f t2)"
-
-primrec preorder :: "'a bt => 'a list" where
-  "preorder Lf = []"
-| "preorder (Br a t1 t2) = [a] @ (preorder t1) @ (preorder t2)"
-
-primrec inorder :: "'a bt => 'a list" where
-  "inorder Lf = []"
-| "inorder (Br a t1 t2) = (inorder t1) @ [a] @ (inorder t2)"
-
-primrec postorder :: "'a bt => 'a list" where
-  "postorder Lf = []"
-| "postorder (Br a t1 t2) = (postorder t1) @ (postorder t2) @ [a]"
-
-primrec append :: "'a bt => 'a bt => 'a bt" where
-  "append Lf t = t"
-| "append (Br a t1 t2) t = Br a (append t1 t) (append t2 t)"
-
-text {* \medskip BT simplification *}
-
-lemma n_leaves_reflect: "n_leaves (reflect t) = n_leaves t"
-  apply (induct t)
-   apply auto
-  done
-
-lemma n_nodes_reflect: "n_nodes (reflect t) = n_nodes t"
-  apply (induct t)
-   apply auto
-  done
-
-lemma depth_reflect: "depth (reflect t) = depth t"
-  apply (induct t) 
-   apply auto
-  done
-
-text {*
-  The famous relationship between the numbers of leaves and nodes.
-*}
-
-lemma n_leaves_nodes: "n_leaves t = Suc (n_nodes t)"
-  apply (induct t)
-   apply auto
-  done
-
-lemma reflect_reflect_ident: "reflect (reflect t) = t"
-  apply (induct t)
-   apply auto
-  done
-
-lemma bt_map_reflect: "bt_map f (reflect t) = reflect (bt_map f t)"
-  apply (induct t)
-   apply simp_all
-  done
-
-lemma preorder_bt_map: "preorder (bt_map f t) = map f (preorder t)"
-  apply (induct t)
-   apply simp_all
-  done
-
-lemma inorder_bt_map: "inorder (bt_map f t) = map f (inorder t)"
-  apply (induct t)
-   apply simp_all
-  done
-
-lemma postorder_bt_map: "postorder (bt_map f t) = map f (postorder t)"
-  apply (induct t)
-   apply simp_all
-  done
-
-lemma depth_bt_map [simp]: "depth (bt_map f t) = depth t"
-  apply (induct t)
-   apply simp_all
-  done
-
-lemma n_leaves_bt_map [simp]: "n_leaves (bt_map f t) = n_leaves t"
-  apply (induct t)
-   apply (simp_all add: distrib_right)
-  done
-
-lemma preorder_reflect: "preorder (reflect t) = rev (postorder t)"
-  apply (induct t)
-   apply simp_all
-  done
-
-lemma inorder_reflect: "inorder (reflect t) = rev (inorder t)"
-  apply (induct t)
-   apply simp_all
-  done
-
-lemma postorder_reflect: "postorder (reflect t) = rev (preorder t)"
-  apply (induct t)
-   apply simp_all
-  done
-
-text {*
- Analogues of the standard properties of the append function for lists.
-*}
-
-lemma append_assoc [simp]:
-     "append (append t1 t2) t3 = append t1 (append t2 t3)"
-  apply (induct t1)
-   apply simp_all
-  done
-
-lemma append_Lf2 [simp]: "append t Lf = t"
-  apply (induct t)
-   apply simp_all
-  done
-
-lemma depth_append [simp]: "depth (append t1 t2) = depth t1 + depth t2"
-  apply (induct t1)
-   apply (simp_all add: max_add_distrib_left)
-  done
-
-lemma n_leaves_append [simp]:
-     "n_leaves (append t1 t2) = n_leaves t1 * n_leaves t2"
-  apply (induct t1)
-   apply (simp_all add: distrib_right)
-  done
-
-lemma bt_map_append:
-     "bt_map f (append t1 t2) = append (bt_map f t1) (bt_map f t2)"
-  apply (induct t1)
-   apply simp_all
-  done
-
-end