reserve E, x, y, X for set;
reserve A, B, C, D for Subset of E^omega;
reserve a, a1, a2, b, c, c1, c2, d, ab, bc for Element of E^omega;
reserve e for Element of E;
reserve i, j, k, l, n, n1, n2, m for Nat;

theorem
  A |^ (m + 1) c= (A*) ^^ A & A |^ (m + 1) c= A ^^ (A*)
by Th50;
