--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Relation.thy Fri May 26 18:11:47 1995 +0200
@@ -0,0 +1,27 @@
+(* Title: Relation.thy
+ ID: $Id$
+ Author: Riccardo Mattolini, Dip. Sistemi e Informatica
+ and Lawrence C Paulson, Cambridge University Computer Laboratory
+ Copyright 1994 Universita' di Firenze
+ Copyright 1993 University of Cambridge
+*)
+
+Relation = Prod +
+consts
+ id :: "('a * 'a)set" (*the identity relation*)
+ O :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60)
+ trans :: "('a * 'a)set => bool" (*transitivity predicate*)
+ converse :: "('a*'a) set => ('a*'a) set"
+ "^^" :: "[('a*'a) set,'a set] => 'a set" (infixl 90)
+ Domain :: "('a*'a) set => 'a set"
+ Range :: "('a*'a) set => 'a set"
+defs
+ id_def "id == {p. ? x. p = (x,x)}"
+ comp_def (*composition of relations*)
+ "r O s == {xz. ? x y z. xz = (x,z) & (x,y):s & (y,z):r}"
+ trans_def "trans(r) == (!x y z. (x,y):r --> (y,z):r --> (x,z):r)"
+ converse_def "converse(r) == {z. (? w:r. ? x y. w=(x,y) & z=(y,x))}"
+ Domain_def "Domain(r) == {z. ! x. (z=x --> (? y. (x,y):r))}"
+ Range_def "Range(r) == Domain(converse(r))"
+ Image_def "r ^^ s == {y. y:Range(r) & (? x:s. (x,y):r)}"
+end