
theorem
  for L be continuous sup-Semilattice holds [#]L is CLbasis of L
proof
  let L be continuous sup-Semilattice;
  now
    let x be Element of L;
    waybelow x /\ [#]L = waybelow x by XBOOLE_1:28;
    hence x = sup (waybelow x /\ [#]L) by WAYBEL_3:def 5;
  end;
  hence thesis by WAYBEL23:def 7;
end;
