src/ZF/Ordinal.thy
author clasohm
Tue, 06 Feb 1996 12:27:17 +0100
changeset 1478 2b8c2a7547ab
parent 1401 0c439768f45c
child 2469 b50b8c0eec01
permissions -rw-r--r--
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(*  Title:      ZF/Ordinal.thy
    ID:         $Id$
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
    Copyright   1994  University of Cambridge

Ordinals in Zermelo-Fraenkel Set Theory 
*)

Ordinal = WF + Bool + "simpdata" + "equalities" +
consts
  Memrel        :: i=>i
  Transset,Ord  :: i=>o
  "<"           :: [i,i] => o  (infixl 50) (*less than on ordinals*)
  "le"          :: [i,i] => o  (infixl 50) (*less than or equals*)
  Limit         :: i=>o

translations
  "x le y"      == "x < succ(y)"

defs
  Memrel_def    "Memrel(A)   == {z: A*A . EX x y. z=<x,y> & x:y }"
  Transset_def  "Transset(i) == ALL x:i. x<=i"
  Ord_def       "Ord(i)      == Transset(i) & (ALL x:i. Transset(x))"
  lt_def        "i<j         == i:j & Ord(j)"
  Limit_def     "Limit(i)    == Ord(i) & 0<i & (ALL y. y<i --> succ(y)<i)"

end