reserve Y for non empty set;
reserve Y for non empty set;
reserve Y for non empty set;

theorem
  for a,b being Function of Y,BOOLEAN holds a 'xor' b = 'not' a
  'xor' 'not' b
proof
  let a,b be Function of Y,BOOLEAN;
    let x be Element of Y;
    ('not' a 'xor' 'not' b).x =(('not' 'not' a '&' 'not' b) 'or' ('not' a
    '&' 'not' 'not' b)).x by BVFUNC_4:9
      .=(a 'xor' b).x by BVFUNC_4:9;
    hence thesis;
end;
