reserve E, x, y, X for set;
reserve A, B, C, D for Subset of E^omega;
reserve a, a1, a2, b, c, c1, c2, d, ab, bc for Element of E^omega;
reserve e for Element of E;
reserve i, j, k, l, n, n1, n2, m for Nat;

theorem
  (A |^ n) \/ (B |^ n) c= (A \/ B) |^ n
proof
  A |^ n c= (A \/ B) |^ n & B |^ n c= (A \/ B) |^ n by Th37,XBOOLE_1:7;
  hence thesis by XBOOLE_1:8;
end;
