--- a/src/HOL/Relation.thy Thu Oct 21 19:00:25 1999 +0200
+++ b/src/HOL/Relation.thy Fri Oct 22 17:04:19 1999 +0200
@@ -6,21 +6,20 @@
Relation = Prod +
-consts
- O :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60)
- converse :: "('a*'b) set => ('b*'a) set" ("(_^-1)" [1000] 999)
- "^^" :: "[('a*'b) set,'a set] => 'b set" (infixl 90)
-
-defs
- comp_def "r O s == {(x,z). ? y. (x,y):s & (y,z):r}"
- converse_def "r^-1 == {(y,x). (x,y):r}"
- Image_def "r ^^ s == {y. ? x:s. (x,y):r}"
-
constdefs
- Id :: "('a * 'a)set" (*the identity relation*)
- "Id == {p. ? x. p = (x,x)}"
+ converse :: "('a*'b) set => ('b*'a) set" ("(_^-1)" [1000] 999)
+ "r^-1 == {(y,x). (x,y):r}"
+
+ comp :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr "O" 60)
+ "r O s == {(x,z). ? y. (x,y):s & (y,z):r}"
- diag :: "'a set => ('a * 'a)set"
+ Image :: "[('a*'b) set,'a set] => 'b set" (infixl "^^" 90)
+ "r ^^ s == {y. ? x:s. (x,y):r}"
+
+ Id :: "('a * 'a)set" (*the identity relation*)
+ "Id == {p. ? x. p = (x,x)}"
+
+ diag :: "'a set => ('a * 'a)set" (*diagonal: identity over a set*)
"diag(A) == UN x:A. {(x,x)}"
Domain :: "('a*'b) set => 'a set"