reserve Y for non empty set;
reserve B for Subset of Y;

theorem Th4:
  for a being Function of Y,BOOLEAN holds a '&' O_el(Y)=O_el( Y)
proof
  let a be Function of Y,BOOLEAN;
  let x be Element of Y;
  thus (a '&' O_el(Y)).x = a.x '&' (O_el Y).x by MARGREL1:def 20
        .= a.x '&' FALSE by Def10
        .= O_el(Y).x by Def10;
end;
