reserve Y for non empty set;

theorem
  for a,b being Function of Y,BOOLEAN
    holds a 'xor' b = ('not' a '&' b) 'or' (a '&' 'not' b)
proof
  let a,b be Function of Y,BOOLEAN;
  let x be Element of Y;
  thus (a 'xor' b).x = a.x 'xor' b.x by BVFUNC_1:def 5
     .= 'not' a.x '&' b.x 'or' a.x '&' 'not' b.x
     .= 'not' a.x '&' b.x 'or' a.x '&' ('not' b).x by MARGREL1:def 19
     .= ('not' a).x '&' b.x 'or' a.x '&' ('not' b).x by MARGREL1:def 19
     .= ('not' a '&' b).x 'or' a.x '&' ('not' b).x by MARGREL1:def 20
     .= ('not' a '&' b).x 'or' (a '&' 'not' b).x by MARGREL1:def 20
     .= (('not' a '&' b) 'or' (a '&' 'not' b)).x by BVFUNC_1:def 4;
end;
