src/ZF/Order.thy
 changeset 435 ca5356bd315a child 578 efc648d29dd0
```--- /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```