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 |^ k) |^ (m, n) c= (A |^ (m, n)) |^ k
proof
  (A |^ (m, n)) |^ k = A |^ (m * k, n * k) by Th40;
  hence thesis by Th42;
end;
