src/ZF/Bool.thy
author clasohm
Thu Sep 16 12:20:38 1993 +0200 (1993-09-16 ago)
changeset 0 a5a9c433f639
child 14 1c0926788772
permissions -rw-r--r--
Initial revision
clasohm@0
     1
(*  Title: 	ZF/bool.thy
clasohm@0
     2
    ID:         $Id$
clasohm@0
     3
    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
clasohm@0
     4
    Copyright   1992  University of Cambridge
clasohm@0
     5
clasohm@0
     6
Booleans in Zermelo-Fraenkel Set Theory 
clasohm@0
     7
*)
clasohm@0
     8
clasohm@0
     9
Bool = ZF +
clasohm@0
    10
consts
clasohm@0
    11
    "1"		::      "i"     	("1")
clasohm@0
    12
    bool        ::      "i"
clasohm@0
    13
    cond        ::      "[i,i,i]=>i"
clasohm@0
    14
    not		::	"i=>i"
clasohm@0
    15
    and         ::      "[i,i]=>i"      (infixl 70)
clasohm@0
    16
    or		::      "[i,i]=>i"      (infixl 65)
clasohm@0
    17
    xor		::      "[i,i]=>i"      (infixl 65)
clasohm@0
    18
clasohm@0
    19
rules
clasohm@0
    20
    one_def 	"1    == succ(0)"
clasohm@0
    21
    bool_def	"bool == {0,1}"
clasohm@0
    22
    cond_def	"cond(b,c,d) == if(b=1,c,d)"
clasohm@0
    23
    not_def	"not(b) == cond(b,0,1)"
clasohm@0
    24
    and_def	"a and b == cond(a,b,0)"
clasohm@0
    25
    or_def	"a or b == cond(a,1,b)"
clasohm@0
    26
    xor_def	"a xor b == cond(a,not(b),b)"
clasohm@0
    27
end