
theorem Seven1:
  for T being with_equivalence naturally_generated non empty TopRelStr,
      A being Subset of T holds
    Kurat7Set A = { A, Cl A, Int A }
  proof
    let T be with_equivalence naturally_generated non empty TopRelStr,
        A be Subset of T;
A1: Cl Int Cl A = Cl A by ROUGHS_1:30;
    Kurat7Set A = { A } \/ { Int A, Int Cl A, Int Cl Int A } \/ { Cl A, Cl
     Int A, Cl Int Cl A } by KURATO_1:8
     .= { A } \/ { Int A, Int Cl A, Int A } \/ { Cl A, Cl
     Int A, Cl Int Cl A } by ROUGHS_1:31
      .= { A } \/ { Int A, Int A, Int Cl A } \/
         { Cl A, Cl Int A, Cl A } by ENUMSET1:57,A1
      .= { A } \/ { Int A, Int Cl A } \/
         { Cl A, Cl Int A, Cl A } by ENUMSET1:30
      .= { A } \/ { Int A, Int Cl A } \/
         { Cl A, Cl A, Cl Int A } by ENUMSET1:57
      .= { A } \/ { Int A, Int Cl A } \/ { Cl A, Cl Int A } by ENUMSET1:30
      .= { A } \/ { Int A, Cl Cl A } \/ { Cl A, Cl Int A } by ROUGHS_1:36
      .= { A } \/ { Int A, Cl A } \/ { Cl A, Int Int A } by ROUGHS_1:34
      .= { A } \/ ({ Cl A, Int A } \/ { Cl A, Int A }) by XBOOLE_1:4
      .= { A, Cl A, Int A } by ENUMSET1:2;
    hence thesis;
  end;
