theorem Th7:
  R is closed & S is closed implies Cl(R /\ S) = Cl R /\ Cl S
proof
  assume that
A1: R is closed and
A2: S is closed;
A3: S = Cl S by A2,PRE_TOPC:22;
A4: Cl(R /\ S) c= Cl R /\ Cl S by PRE_TOPC:21;
  R = Cl R by A1,PRE_TOPC:22;
  then Cl R /\ Cl S c= Cl(R /\ S) by A3,PRE_TOPC:18;
  hence thesis by A4;
end;
