src/ZF/bool.thy

canonical 'cases'/'induct' rules for n-tuples (n=3..7)
(really belongs to theory Product_Type, but doesn't work there yet)

(*  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