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 Th90:
  A+ ^^ (A |^.. k) = A |^.. (k + 1)
proof
  thus A+ ^^ (A |^.. k) = (A |^.. 1) ^^ (A |^.. k) by Th50
    .= A |^.. (k + 1) by Th18;
end;
