src/ZF/Bool.thy
author lcp
Fri Dec 16 17:39:43 1994 +0100 (1994-12-16 ago)
changeset 799 13aa1e3d8a3a
parent 753 ec86863e87c8
child 837 778f01546669
permissions -rw-r--r--
put quotation marks around constant "and" because it is a
keyword for inductive definitions!!
     1 (*  Title: 	ZF/bool.thy
     2     ID:         $Id$
     3     Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1992  University of Cambridge
     5 
     6 Booleans in Zermelo-Fraenkel Set Theory 
     7 *)
     8 
     9 Bool = ZF + "simpdata" +
    10 consts
    11     "1"		::      "i"     	("1")
    12     bool        ::      "i"
    13     cond        ::      "[i,i,i]=>i"
    14     not		::	"i=>i"
    15     "and"       ::      "[i,i]=>i"      (infixl 70)
    16     or		::      "[i,i]=>i"      (infixl 65)
    17     xor		::      "[i,i]=>i"      (infixl 65)
    18 
    19 translations
    20    "1"  == "succ(0)"
    21 
    22 defs
    23     bool_def	"bool == {0,1}"
    24     cond_def	"cond(b,c,d) == if(b=1,c,d)"
    25     not_def	"not(b) == cond(b,0,1)"
    26     and_def	"a and b == cond(a,b,0)"
    27     or_def	"a or b == cond(a,1,b)"
    28     xor_def	"a xor b == cond(a,not(b),b)"
    29 end