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?) ^^ (A |^ (m, n)) = (A |^ (m, n)) ^^ (A?)
proof
  (A |^ (0, 1)) ^^ (A |^ (m, n)) = (A |^ (m, n)) ^^ (A |^ (0, 1)) by Th39;
  then (A?) ^^ (A |^ (m, n)) = (A |^ (m, n)) ^^ (A |^ (0, 1)) by Th79;
  hence thesis by Th79;
end;
