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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 1992 University of Cambridge
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Natural numbers in Zermelo-Fraenkel Set Theory
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*)
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Nat = Ord + Bool +
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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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rules
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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(k,a,b) == 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(n, a, %m. b(m, f`m)))"
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end
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