src/ZF/Ordinal.thy
changeset 435 ca5356bd315a
child 753 ec86863e87c8
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/src/ZF/Ordinal.thy	Tue Jun 21 17:20:34 1994 +0200
     1.3 @@ -0,0 +1,28 @@
     1.4 +(*  Title: 	ZF/Ordinal.thy
     1.5 +    ID:         $Id$
     1.6 +    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
     1.7 +    Copyright   1994  University of Cambridge
     1.8 +
     1.9 +Ordinals in Zermelo-Fraenkel Set Theory 
    1.10 +*)
    1.11 +
    1.12 +Ordinal = WF + "simpdata" + "equalities" +
    1.13 +consts
    1.14 +  Memrel      	:: "i=>i"
    1.15 +  Transset,Ord  :: "i=>o"
    1.16 +  "<"           :: "[i,i] => o"  (infixl 50) (*less than on ordinals*)
    1.17 +  "le"          :: "[i,i] => o"  (infixl 50) (*less than or equals*)
    1.18 +  Limit         :: "i=>o"
    1.19 +
    1.20 +translations
    1.21 +  "x le y"      == "x < succ(y)"
    1.22 +
    1.23 +rules
    1.24 +  Memrel_def  	"Memrel(A)   == {z: A*A . EX x y. z=<x,y> & x:y }"
    1.25 +  Transset_def	"Transset(i) == ALL x:i. x<=i"
    1.26 +  Ord_def     	"Ord(i)      == Transset(i) & (ALL x:i. Transset(x))"
    1.27 +  lt_def        "i<j         == i:j & Ord(j)"
    1.28 +  Limit_def     "Limit(i)    == Ord(i) & 0<i & (ALL y. y<i --> succ(y)<i)"
    1.29 +
    1.30 +
    1.31 +end