src/ZF/Ordinal.thy
 author paulson Fri Jan 03 15:01:55 1997 +0100 (1997-01-03) changeset 2469 b50b8c0eec01 parent 1478 2b8c2a7547ab child 2539 ddd22ceee8cc permissions -rw-r--r--
Implicit simpsets and clasets for FOL and ZF
```     1 (*  Title:      ZF/Ordinal.thy
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```     2     ID:         \$Id\$
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```     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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```     4     Copyright   1994  University of Cambridge
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```     5
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```     6 Ordinals in Zermelo-Fraenkel Set Theory
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```     7 *)
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```     8
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```     9 Ordinal = WF + Bool + equalities +
```
```    10 consts
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```    11   Memrel        :: i=>i
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```    12   Transset,Ord  :: i=>o
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```    13   "<"           :: [i,i] => o  (infixl 50) (*less than on ordinals*)
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```    14   "le"          :: [i,i] => o  (infixl 50) (*less than or equals*)
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```    15   Limit         :: i=>o
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```    16
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```    17 translations
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```    18   "x le y"      == "x < succ(y)"
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```    19
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```    20 defs
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```    21   Memrel_def    "Memrel(A)   == {z: A*A . EX x y. z=<x,y> & x:y }"
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```    22   Transset_def  "Transset(i) == ALL x:i. x<=i"
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```    23   Ord_def       "Ord(i)      == Transset(i) & (ALL x:i. Transset(x))"
```
```    24   lt_def        "i<j         == i:j & Ord(j)"
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```    25   Limit_def     "Limit(i)    == Ord(i) & 0<i & (ALL y. y<i --> succ(y)<i)"
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```    26
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```    27 end
```