src/ZF/Ordinal.thy
 author lcp Tue Jun 21 17:20:34 1994 +0200 (1994-06-21) changeset 435 ca5356bd315a child 753 ec86863e87c8 permissions -rw-r--r--
Addition of cardinals and order types, various tidying
```     1 (*  Title: 	ZF/Ordinal.thy
```
```     2     ID:         \$Id\$
```
```     3     Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
```
```     4     Copyright   1994  University of Cambridge
```
```     5
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```     6 Ordinals in Zermelo-Fraenkel Set Theory
```
```     7 *)
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```     8
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```     9 Ordinal = WF + "simpdata" + "equalities" +
```
```    10 consts
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```    11   Memrel      	:: "i=>i"
```
```    12   Transset,Ord  :: "i=>o"
```
```    13   "<"           :: "[i,i] => o"  (infixl 50) (*less than on ordinals*)
```
```    14   "le"          :: "[i,i] => o"  (infixl 50) (*less than or equals*)
```
```    15   Limit         :: "i=>o"
```
```    16
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```    17 translations
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```    18   "x le y"      == "x < succ(y)"
```
```    19
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```    20 rules
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```    21   Memrel_def  	"Memrel(A)   == {z: A*A . EX x y. z=<x,y> & x:y }"
```
```    22   Transset_def	"Transset(i) == ALL x:i. x<=i"
```
```    23   Ord_def     	"Ord(i)      == Transset(i) & (ALL x:i. Transset(x))"
```
```    24   lt_def        "i<j         == i:j & Ord(j)"
```
```    25   Limit_def     "Limit(i)    == Ord(i) & 0<i & (ALL y. y<i --> succ(y)<i)"
```
```    26
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```    27
```
```    28 end
```