reserve E, x, y, X for set;
reserve A, B, C for Subset of E^omega;
reserve a, a1, a2, b for Element of E^omega;
reserve i, k, l, m, n for Nat;

theorem Th57:
  A+ = A* iff <%>E in A
proof
  thus A+ = A* implies <%>E in A
  by FLANG_1:48,Th56;
  assume <%>E in A;
  then A* = (A*) ^^ A by FLANG_1:54;
  hence thesis by Th52;
end;
