src/ZF/Ordinal.thy
author lcp
Thu, 12 Jan 1995 03:01:40 +0100
changeset 852 664052e3cf66
parent 753 ec86863e87c8
child 1401 0c439768f45c
permissions -rw-r--r--
Now depends upon Bool, so that 1 and 2 are defined

(*  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