reserve Y for non empty set;

theorem
  for a,b being Function of Y,BOOLEAN holds a '&' (a 'or' b) = a
proof
  let a,b be Function of Y,BOOLEAN;
  let x be Element of Y;
  thus (a '&' (a 'or' b)).x = a.x '&' (a 'or' b).x by MARGREL1:def 20
     .= a.x '&' (a.x 'or' b.x) by BVFUNC_1:def 4
     .= a.x by XBOOLEAN:6;
end;
