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

theorem
  { Int KurExSet, Int Cl KurExSet, Int Cl Int KurExSet, Cl
  KurExSet, Cl Int KurExSet, Cl Int Cl KurExSet } misses { KurExSet }
proof
  set A = KurExSet;
  assume { Int KurExSet, Int Cl KurExSet, Int Cl Int KurExSet, Cl KurExSet,
  Cl Int KurExSet, Cl Int Cl KurExSet } meets { KurExSet };
  then
A1: KurExSet in { Int KurExSet, Int Cl KurExSet, Int Cl Int KurExSet, Cl
  KurExSet, Cl Int KurExSet, Cl Int Cl KurExSet } by ZFMISC_1:50;
  per cases by A1,ENUMSET1:def 4;
  suppose
    A = Int A;
    hence thesis;
  end;
  suppose
    A = Int Cl A;
    hence thesis;
  end;
  suppose
    A = Int Cl Int A;
    hence thesis;
  end;
  suppose
    A = Cl A;
    hence thesis;
  end;
  suppose
    A = Cl Int A;
    hence thesis;
  end;
  suppose
    A = Cl Int Cl A;
    hence thesis;
  end;
end;
