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 |^ (0, 2) = {<%>E} \/ A \/ (A ^^ A)
proof
  thus A |^ (0, 2) = A |^ (0, 1) \/ A |^ (1 + 1) by Th26
    .= {<%>E} \/ A \/ A |^ (1 + 1) by Th46
    .= {<%>E} \/ A \/ (A ^^ A) by FLANG_1:26;
end;
