src/ZF/Nat.thy
author lcp
Tue, 29 Nov 1994 00:31:31 +0100
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(*  Title: 	ZF/Nat.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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Natural numbers in Zermelo-Fraenkel Set Theory 
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*)
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Nat = Ordinal + Bool + "mono" +
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consts
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    nat 	::      "i"
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    nat_case    ::      "[i, i=>i, i]=>i"
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    nat_rec     ::      "[i, i, [i,i]=>i]=>i"
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defs
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    nat_def     "nat == lfp(Inf, %X. {0} Un {succ(i). i:X})"
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    nat_case_def
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	"nat_case(a,b,k) == THE y. k=0 & y=a | (EX x. k=succ(x) & y=b(x))"
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    nat_rec_def
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	"nat_rec(k,a,b) ==   \
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\   	  wfrec(Memrel(nat), k, %n f. nat_case(a, %m. b(m, f`m), n))"
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end