--- a/src/HOL/Library/Tree.thy Wed Jun 17 10:57:11 2015 +0200
+++ b/src/HOL/Library/Tree.thy Wed Jun 17 11:03:05 2015 +0200
@@ -1,6 +1,6 @@
(* Author: Tobias Nipkow *)
-section {* Binary Tree *}
+section \<open>Binary Tree\<close>
theory Tree
imports Main
@@ -14,7 +14,7 @@
| "right Leaf = Leaf"
datatype_compat tree
-text{* Can be seen as counting the number of leaves rather than nodes: *}
+text\<open>Can be seen as counting the number of leaves rather than nodes:\<close>
definition size1 :: "'a tree \<Rightarrow> nat" where
"size1 t = size t + 1"
@@ -92,13 +92,13 @@
by (induction t) auto
-subsection {* Binary Search Tree predicate *}
+subsection \<open>Binary Search Tree predicate\<close>
fun (in linorder) bst :: "'a tree \<Rightarrow> bool" where
"bst \<langle>\<rangle> \<longleftrightarrow> True" |
"bst \<langle>l, a, r\<rangle> \<longleftrightarrow> bst l \<and> bst r \<and> (\<forall>x\<in>set_tree l. x < a) \<and> (\<forall>x\<in>set_tree r. a < x)"
-text{* In case there are duplicates: *}
+text\<open>In case there are duplicates:\<close>
fun (in linorder) bst_eq :: "'a tree \<Rightarrow> bool" where
"bst_eq \<langle>\<rangle> \<longleftrightarrow> True" |