--- a/src/HOL/ex/PER.thy Sat May 27 17:42:00 2006 +0200
+++ b/src/HOL/ex/PER.thy Sat May 27 17:42:02 2006 +0200
@@ -44,9 +44,9 @@
\emph{any} other one.
*}
-constdefs
- domain :: "'a::partial_equiv set"
- "domain == {x. x \<sim> x}"
+definition
+ "domain" :: "'a::partial_equiv set"
+ "domain = {x. x \<sim> x}"
lemma domainI [intro]: "x \<sim> x ==> x \<in> domain"
by (unfold domain_def) blast
@@ -164,9 +164,9 @@
representation of elements of a quotient type.
*}
-constdefs
+definition
eqv_class :: "('a::partial_equiv) => 'a quot" ("\<lfloor>_\<rfloor>")
- "\<lfloor>a\<rfloor> == Abs_quot {x. a \<sim> x}"
+ "\<lfloor>a\<rfloor> = Abs_quot {x. a \<sim> x}"
theorem quot_rep: "\<exists>a. A = \<lfloor>a\<rfloor>"
proof (cases A)
@@ -231,9 +231,9 @@
subsection {* Picking representing elements *}
-constdefs
+definition
pick :: "'a::partial_equiv quot => 'a"
- "pick A == SOME a. A = \<lfloor>a\<rfloor>"
+ "pick A = (SOME a. A = \<lfloor>a\<rfloor>)"
theorem pick_eqv' [intro?, simp]: "a \<in> domain ==> pick \<lfloor>a\<rfloor> \<sim> a"
proof (unfold pick_def)