theorem
  Cl Int Cl(meet F) c= meet(Cl Int Cl F)
proof
A1: Cl Int Cl(meet F) c= Cl(meet Int Cl F) by Th51,PRE_TOPC:19;
  Cl(meet Int Cl F) c= meet(Cl Int Cl F) by Th14;
  hence thesis by A1;
end;
