reserve Y for TopStruct;

theorem
  for A, B being Subset of Y holds A is discrete or B is discrete
  implies A /\ B is discrete
proof
  let A, B be Subset of Y;
  assume
A1: A is discrete or B is discrete;
  hereby
    per cases by A1;
    suppose
      A is discrete;
      hence thesis by Th22,XBOOLE_1:17;
    end;
    suppose
      B is discrete;
      hence thesis by Th22,XBOOLE_1:17;
    end;
  end;
end;
