theorem
  R is dense & R c= S implies S is dense
proof
  assume that
A1: R is dense and
A2: R c= S;
  Cl R = [#] GX by A1;
  then [#] GX c= Cl S by A2,PRE_TOPC:19;
  then [#] GX = Cl S;
  hence thesis;
end;
