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 Th23:
  (R is open implies Int R = R) & (Int P = P implies P is open)
proof
  hereby
    assume R is open;
    then R` is closed by Th4;
    then Cl R` = R` by PRE_TOPC:22;
    hence Int R = R;
  end;
  thus thesis;
end;
