src/ZF/bool.thy
author clasohm
Thu, 16 Sep 1993 12:20:38 +0200
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(*  Title: 	ZF/bool.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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Booleans in Zermelo-Fraenkel Set Theory 
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*)
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Bool = ZF +
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consts
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    "1"		::      "i"     	("1")
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    bool        ::      "i"
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    cond        ::      "[i,i,i]=>i"
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    not		::	"i=>i"
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    and         ::      "[i,i]=>i"      (infixl 70)
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    or		::      "[i,i]=>i"      (infixl 65)
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    xor		::      "[i,i]=>i"      (infixl 65)
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rules
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    one_def 	"1    == succ(0)"
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    bool_def	"bool == {0,1}"
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    cond_def	"cond(b,c,d) == if(b=1,c,d)"
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    not_def	"not(b) == cond(b,0,1)"
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    and_def	"a and b == cond(a,b,0)"
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    or_def	"a or b == cond(a,1,b)"
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    xor_def	"a xor b == cond(a,not(b),b)"
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end