src/HOL/Library/Tree_Multiset.thy
author wenzelm
Mon Dec 28 01:28:28 2015 +0100 (2015-12-28)
changeset 61945 1135b8de26c3
parent 60808 fd26519b1a6a
child 63861 90360390a916
permissions -rw-r--r--
more symbols;
     1 (* Author: Tobias Nipkow *)
     2 
     3 section \<open>Multiset of Elements of Binary Tree\<close>
     4 
     5 theory Tree_Multiset
     6 imports Multiset Tree
     7 begin
     8 
     9 text\<open>Kept separate from theory @{theory Tree} to avoid importing all of
    10 theory @{theory Multiset} into @{theory Tree}. Should be merged if
    11 @{theory Multiset} ever becomes part of @{theory Main}.\<close>
    12 
    13 fun mset_tree :: "'a tree \<Rightarrow> 'a multiset" where
    14 "mset_tree Leaf = {#}" |
    15 "mset_tree (Node l a r) = {#a#} + mset_tree l + mset_tree r"
    16 
    17 lemma set_mset_tree[simp]: "set_mset (mset_tree t) = set_tree t"
    18 by(induction t) auto
    19 
    20 lemma size_mset_tree[simp]: "size(mset_tree t) = size t"
    21 by(induction t) auto
    22 
    23 lemma mset_map_tree: "mset_tree (map_tree f t) = image_mset f (mset_tree t)"
    24 by (induction t) auto
    25 
    26 lemma mset_iff_set_tree: "x \<in># mset_tree t \<longleftrightarrow> x \<in> set_tree t"
    27 by(induction t arbitrary: x) auto
    28 
    29 lemma mset_preorder[simp]: "mset (preorder t) = mset_tree t"
    30 by (induction t) (auto simp: ac_simps)
    31 
    32 lemma mset_inorder[simp]: "mset (inorder t) = mset_tree t"
    33 by (induction t) (auto simp: ac_simps)
    34 
    35 lemma map_mirror: "mset_tree (mirror t) = mset_tree t"
    36 by (induction t) (simp_all add: ac_simps)
    37 
    38 end