reserve T for non empty TopSpace;
reserve A for Subset of T;

theorem Th1:
  A-`-`-`- = A-`-
proof
  set B = Cl (Cl A)`;
  set U = (Cl A)`;
  U = Int U by TOPS_1:23;
  then U c= Int Cl U by PRE_TOPC:18,TOPS_1:19;
  then Cl Int B c= Cl B & Cl U c= Cl Int Cl U by PRE_TOPC:19,TOPS_1:16;
  then Cl Int B = B by XBOOLE_0:def 10;
  hence thesis by TOPS_1:def 1;
end;
