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src/ZF/Bool.thy
author wenzelm
Fri, 19 Aug 1994 15:41:39 +0200
changeset 564 eec3a9222b50
parent 124 858ab9a9b047
child 753 ec86863e87c8
permissions -rw-r--r--
added inferT_axm; removed extend_theory; changed read_def_cterm: now uses Sign.infer_types;

(*  Title: 	ZF/bool.thy
    ID:         $Id$
    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
    Copyright   1992  University of Cambridge

Booleans in Zermelo-Fraenkel Set Theory 
*)

Bool = ZF + "simpdata" +
consts
    "1"		::      "i"     	("1")
    bool        ::      "i"
    cond        ::      "[i,i,i]=>i"
    not		::	"i=>i"
    and         ::      "[i,i]=>i"      (infixl 70)
    or		::      "[i,i]=>i"      (infixl 65)
    xor		::      "[i,i]=>i"      (infixl 65)

translations
   "1"  == "succ(0)"

rules
    bool_def	"bool == {0,1}"
    cond_def	"cond(b,c,d) == if(b=1,c,d)"
    not_def	"not(b) == cond(b,0,1)"
    and_def	"a and b == cond(a,b,0)"
    or_def	"a or b == cond(a,1,b)"
    xor_def	"a xor b == cond(a,not(b),b)"
end
isabelle