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
  A+ ^^ (A+) = A |^.. 2
proof
  thus A+ ^^ (A+) = A |^.. 1 ^^ (A+) by Th50
    .= A |^.. 1 ^^ (A |^.. 1) by Th50
    .= A |^.. (1 + 1) by Th18
    .= A |^.. 2;
end;
