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(* Title: ZF/Ordinal.thy
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ID: $Id$
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory
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Copyright 1994 University of Cambridge
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Ordinals in Zermelo-Fraenkel Set Theory
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*)
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Ordinal = WF + Bool + equalities +
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consts
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Memrel :: i=>i
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Transset,Ord :: i=>o
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"<" :: [i,i] => o (infixl 50) (*less than on ordinals*)
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Limit :: i=>o
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syntax
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"le" :: [i,i] => o (infixl 50) (*less than or equals*)
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translations
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"x le y" == "x < succ(y)"
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syntax (symbols)
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"op le" :: [i,i] => o (infixl "\\<le>" 50) (*less than or equals*)
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defs
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Memrel_def "Memrel(A) == {z: A*A . EX x y. z=<x,y> & x:y }"
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Transset_def "Transset(i) == ALL x:i. x<=i"
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Ord_def "Ord(i) == Transset(i) & (ALL x:i. Transset(x))"
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lt_def "i<j == i:j & Ord(j)"
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Limit_def "Limit(i) == Ord(i) & 0<i & (ALL y. y<i --> succ(y)<i)"
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end
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