theorem
  P is open_condensed & Q is open_condensed implies P /\ Q is open_condensed
proof
A1: P` \/ Q` = (P /\ Q)` by XBOOLE_1:54;
  assume that
A2: P is open_condensed and
A3: Q is open_condensed;
A4: Q` is closed_condensed by A3;
  P` is closed_condensed by A2;
  then P` \/ Q` is closed_condensed by A4,Th68;
  hence thesis by A1;
end;
