--- a/src/HOL/ex/PER.thy Fri Nov 17 02:19:55 2006 +0100
+++ b/src/HOL/ex/PER.thy Fri Nov 17 02:20:03 2006 +0100
@@ -45,7 +45,7 @@
*}
definition
- "domain" :: "'a::partial_equiv set"
+ "domain" :: "'a::partial_equiv set" where
"domain = {x. x \<sim> x}"
lemma domainI [intro]: "x \<sim> x ==> x \<in> domain"
@@ -165,7 +165,7 @@
*}
definition
- eqv_class :: "('a::partial_equiv) => 'a quot" ("\<lfloor>_\<rfloor>")
+ eqv_class :: "('a::partial_equiv) => 'a quot" ("\<lfloor>_\<rfloor>") where
"\<lfloor>a\<rfloor> = Abs_quot {x. a \<sim> x}"
theorem quot_rep: "\<exists>a. A = \<lfloor>a\<rfloor>"
@@ -232,7 +232,7 @@
subsection {* Picking representing elements *}
definition
- pick :: "'a::partial_equiv quot => 'a"
+ pick :: "'a::partial_equiv quot => 'a" where
"pick A = (SOME a. A = \<lfloor>a\<rfloor>)"
theorem pick_eqv' [intro?, simp]: "a \<in> domain ==> pick \<lfloor>a\<rfloor> \<sim> a"