--- a/src/HOL/Enum.thy Fri Oct 14 18:55:29 2011 +0200
+++ b/src/HOL/Enum.thy Fri Oct 14 18:55:59 2011 +0200
@@ -370,37 +370,6 @@
end
-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
-
instantiation nibble :: enum
begin