--- a/src/HOL/Quotient_Examples/Lift_Set.thy Sat Dec 24 15:53:10 2011 +0100
+++ b/src/HOL/Quotient_Examples/Lift_Set.thy Sat Dec 24 15:53:10 2011 +0100
@@ -8,9 +8,9 @@
imports Main
begin
-definition set where "set = (UNIV :: ('a => bool) => bool)"
+definition set where "set = (UNIV :: ('a \<Rightarrow> bool) set)"
-typedef (open) 'a set = "set :: 'a set set"
+typedef (open) 'a set = "set :: ('a \<Rightarrow> bool) set"
morphisms member Set
unfolding set_def by auto
@@ -37,15 +37,19 @@
text {* Now, we can employ quotient_definition to lift definitions. *}
quotient_definition empty where "empty :: 'a set"
-is "Set.empty"
+is "bot :: 'a \<Rightarrow> bool"
term "Lift_Set.empty"
thm Lift_Set.empty_def
+definition insertp :: "'a \<Rightarrow> ('a \<Rightarrow> bool) \<Rightarrow> 'a \<Rightarrow> bool" where
+ "insertp x P y \<longleftrightarrow> y = x \<or> P y"
+
quotient_definition insert where "insert :: 'a => 'a set => 'a set"
-is "Set.insert"
+is insertp
term "Lift_Set.insert"
thm Lift_Set.insert_def
end
+