src/ZF/Bool.thy

Implicit simpsets and clasets for FOL and ZF

(*  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 

2 is equal to bool, but serves a different purpose
*)

Bool = upair + 
consts
    "1"         :: i             ("1")
    "2"         :: i             ("2")
    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)"
   "2"  == "succ(1)"

defs
    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