--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/ZF/Order.thy Tue Jun 21 17:20:34 1994 +0200
@@ -0,0 +1,31 @@
+(* Title: ZF/Order.thy
+ ID: $Id$
+ Author: Lawrence C Paulson, Cambridge University Computer Laboratory
+ Copyright 1994 University of Cambridge
+
+Orders in Zermelo-Fraenkel Set Theory
+*)
+
+Order = WF + Perm +
+consts
+ part_ord :: "[i,i]=>o" (*Strict partial ordering*)
+ linear, tot_ord :: "[i,i]=>o" (*Strict total ordering*)
+ well_ord :: "[i,i]=>o" (*Well-ordering*)
+ ord_iso :: "[i,i,i,i]=>i" (*Order isomorphisms*)
+ pred :: "[i,i,i]=>i" (*Set of predecessors*)
+
+rules
+ part_ord_def "part_ord(A,r) == irrefl(A,r) & trans[A](r)"
+
+ linear_def "linear(A,r) == (ALL x:A. ALL y:A. <x,y>:r | x=y | <y,x>:r)"
+
+ tot_ord_def "tot_ord(A,r) == part_ord(A,r) & linear(A,r)"
+
+ well_ord_def "well_ord(A,r) == tot_ord(A,r) & wf[A](r)"
+
+ ord_iso_def "ord_iso(A,r,B,s) == \
+\ {f: bij(A,B). ALL x:A. ALL y:A. <x,y>:r <-> <f`x,f`y>:s}"
+
+ pred_def "pred(A,x,r) == {y:A. <y,x>:r}"
+
+end