# HG changeset patch
# User haftmann
# Date 1324738391 -3600
# Node ID 204f34a99cebd20659f6278e39c385b040e628ea
# Parent  deda685ba210cc1fbfbc64990ec3502c67453749
moved `sublists` to theory Enum

diff -r deda685ba210 -r 204f34a99ceb src/HOL/Library/More_List.thy
--- a/src/HOL/Library/More_List.thy	Sat Dec 24 15:53:11 2011 +0100
+++ b/src/HOL/Library/More_List.thy	Sat Dec 24 15:53:11 2011 +0100
@@ -1,4 +1,4 @@
-(*  Author:  Florian Haftmann, TU Muenchen *)
+(* Author:  Florian Haftmann, TU Muenchen *)
 
 header {* Operations on lists beyond the standard List theory *}
 
@@ -299,40 +299,6 @@
   by (simp add: nth_map_def)
 
 
-text {* Enumeration of all sublists of a list *}
-
-primrec sublists :: "'a list \<Rightarrow> 'a list list" where
-  "sublists [] = [[]]"
-  | "sublists (x#xs) = (let xss = sublists xs in map (Cons x) xss @ xss)"
-
-lemma length_sublists:
-  "length (sublists xs) = Suc (Suc (0\<Colon>nat)) ^ length xs"
-  by (induct xs) (simp_all add: Let_def)
-
-lemma sublists_powset:
-  "set ` set (sublists xs) = Pow (set xs)"
-proof -
-  have aux: "\<And>x A. set ` Cons x ` A = insert x ` set ` A"
-    by (auto simp add: image_def)
-  have "set (map set (sublists xs)) = Pow (set xs)"
-    by (induct xs)
-      (simp_all add: aux Let_def Pow_insert Un_commute comp_def del: map_map)
-  then show ?thesis by simp
-qed
-
-lemma distinct_set_sublists:
-  assumes "distinct xs"
-  shows "distinct (map set (sublists xs))"
-proof (rule card_distinct)
-  have "finite (set xs)" by rule
-  then have "card (Pow (set xs)) = Suc (Suc 0) ^ card (set xs)" by (rule card_Pow)
-  with assms distinct_card [of xs]
-    have "card (Pow (set xs)) = Suc (Suc 0) ^ length xs" by simp
-  then show "card (set (map set (sublists xs))) = length (map set (sublists xs))"
-    by (simp add: sublists_powset length_sublists)
-qed
-
-
 text {* monad operation *}
 
 definition bind :: "'a list \<Rightarrow> ('a \<Rightarrow> 'b list) \<Rightarrow> 'b list" where