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
```