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

theorem Th9: :: Theorem 2
  A is subcondensed iff A c= Cl Int A
proof
  thus A is subcondensed implies A c= Cl Int A
  by PRE_TOPC:18;
  assume A c= Cl Int A;
  then
A1: Cl A c= Cl Cl Int A by PRE_TOPC:19;
  Cl Int A c= Cl A by PRE_TOPC:19,TOPS_1:16;
  then Cl Int A = Cl A by A1,XBOOLE_0:def 10;
  hence thesis;
end;
