reserve Y for non empty set;

theorem
  for a,b being Function of Y,BOOLEAN holds a 'or' (a '&' b) = a
proof
  let a,b be Function of Y,BOOLEAN;
  let x be Element of Y;
  thus (a 'or' (a '&' b)).x = a.x 'or' (a '&' b).x by BVFUNC_1:def 4
       .= a.x 'or' a.x '&' b.x by MARGREL1:def 20
       .= a.x by XBOOLEAN:5;
end;
