reserve TS for 1-sorted,
  K, Q for Subset of TS;
reserve TS for TopSpace,
  GX for TopStruct,
  x for set,
  P, Q for Subset of TS,
  K , L for Subset of TS,
  R, S for Subset of GX,
  T, W for Subset of GX;

theorem
  R is open implies Cl Int Cl R = Cl R
proof
  assume
A1: R is open;
  then Cl Int Cl R = Cl Int Cl Int R by Th23
    .= Cl Int R by Th26
    .= Cl R by A1,Th23;
  hence thesis;
end;
