--- a/src/HOL/NumberTheory/BijectionRel.thy Fri Nov 17 02:19:55 2006 +0100
+++ b/src/HOL/NumberTheory/BijectionRel.thy Fri Nov 17 02:20:03 2006 +0100
@@ -30,13 +30,15 @@
*}
definition
- bijP :: "('a => 'a => bool) => 'a set => bool"
+ bijP :: "('a => 'a => bool) => 'a set => bool" where
"bijP P F = (\<forall>a b. a \<in> F \<and> P a b --> b \<in> F)"
- uniqP :: "('a => 'a => bool) => bool"
+definition
+ uniqP :: "('a => 'a => bool) => bool" where
"uniqP P = (\<forall>a b c d. P a b \<and> P c d --> (a = c) = (b = d))"
- symP :: "('a => 'a => bool) => bool"
+definition
+ symP :: "('a => 'a => bool) => bool" where
"symP P = (\<forall>a b. P a b = P b a)"
consts