src/HOL/Integ/Relation.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Integ/Relation.thy	Fri Mar 03 12:04:45 1995 +0100
@@ -0,0 +1,24 @@
+(*  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
+
+Functions represented as relations in Higher-Order Set Theory 
+*)
+
+Relation = Trancl +
+consts
+    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
+    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