reserve T for TopSpace,
  A, B for Subset of T;

theorem Th8: :: Theorem 2
  A is supercondensed iff Int Cl A c= A
proof
  thus A is supercondensed implies Int Cl A c= A
  by TOPS_1:16;
  assume Int Cl A c= A;
  then
A1: Int Int Cl A c= Int A by TOPS_1:19;
  Int A c= Int Cl A by PRE_TOPC:18,TOPS_1:19;
  then Int A = Int Cl A by A1,XBOOLE_0:def 10;
  hence thesis;
end;
