src/ZF/Bool.thy

Installation of new simplfier. Previously appeared to set up the old
simplifier to rewrite with the partial ordering [=, something not possible
with the new simplifier. But such rewriting appears not to have actually
been used, and there were few complications. In terms.ML setloop was used
to avoid infinite rewriting with the letrec rule. Congruence rules were
deleted, and an occasional SIMP_TAC had to become asm_simp_tac.

(*  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 +
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)

rules
    one_def 	"1    == succ(0)"
    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