diff r fc77947a7db4 r 1c7e6454883e src/HOL/Enum.thy
 a/src/HOL/Enum.thy Sat Dec 24 15:53:08 2011 +0100
+++ b/src/HOL/Enum.thy Sat Dec 24 15:53:08 2011 +0100
@@ 458,9 +458,58 @@
unfolding enum_ex_option_def enum_ex
by (auto, case_tac x) auto
qed (auto simp add: enum_UNIV enum_option_def, rule option.exhaust, auto intro: simp add: distinct_map enum_distinct)
+end
+
+primrec sublists :: "'a list \ '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\nat)) ^ length xs"
+ by (induct xs) (simp_all add: Let_def)
+
+lemma sublists_powset:
+ "set ` set (sublists xs) = Pow (set xs)"
+proof 
+ have aux: "\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 set :: (enum) enum
+begin
+
+definition
+ "enum = map set (sublists enum)"
+
+definition
+ "enum_all P \ (\A\set enum. P (A::'a set))"
+
+definition
+ "enum_ex P \ (\A\set enum. P (A::'a set))"
+
+instance proof
+qed (simp_all add: enum_set_def enum_all_set_def enum_ex_set_def sublists_powset distinct_set_sublists
+ enum_distinct enum_UNIV)
end
+
subsection {* Small finite types *}
text {* We define small finite types for the use in Quickcheck *}
@@ 728,12 +777,6 @@
qed
subsection {* Transitive closure on relations over finite types *}

lemma [code]: "trancl (R :: (('a :: enum) \ 'a) set) = ntrancl (length (filter R enum)  1) R"
 by (simp add: finite_trancl_ntranl distinct_length_filter [OF enum_distinct] enum_UNIV Collect_def)


subsection {* Closing up *}
code_abort enum_the