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

theorem Th4:
  A` in Kurat14Set A & A`- in Kurat14Set A & A`-` in Kurat14Set A &
A`-`- in Kurat14Set A & A`-`-` in Kurat14Set A & A`-`-`- in Kurat14Set A & A`-`
  -`-` in Kurat14Set A
proof
A1: Cl A` in Kurat14Part A` & (Cl A`)` in Kurat14Part A` by ENUMSET1:def 5;
A2: Cl (Cl A`)` in Kurat14Part A` & (Cl (Cl A`)`)` in Kurat14Part A` by
ENUMSET1:def 5;
A3: Cl (Cl (Cl A`)`)` in Kurat14Part A` & (Cl (Cl (Cl A`)`)`)` in
  Kurat14Part A` by ENUMSET1:def 5;
  Kurat14Part A` c= Kurat14Set A & A` in Kurat14Part A` by ENUMSET1:def 5
,XBOOLE_1:7;
  hence thesis by A1,A2,A3;
end;
