src/ZF/Bool.thy
author lcp
Fri, 23 Dec 1994 16:49:48 +0100
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Re-indented declarations; declared the number 2
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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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2 is equal to bool, but serves a different purpose
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*)
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Bool = ZF + "simpdata" +
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consts
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    "1"		:: "i"     	   ("1")
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    "2"         :: "i"             ("2")
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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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translations
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   "1"  == "succ(0)"
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   "2"  == "succ(1)"
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defs
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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