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

theorem
  A? |^ (m, n) c= A*
proof
  per cases;
  suppose
    m <= n;
    then A? |^ (m, n) = A |^ (0, n) by Th98;
    hence thesis by Th32;
  end;
  suppose
    m > n;
    then A? |^ (m, n) = {} by Th21;
    hence thesis;
  end;
end;
