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
  (x in A or x in B) & x <> <%>E implies A ^^ B <> {<%>E}
proof
  assume ( x in A or x in B)& x <> <%>E;
  then A <> {<%>E} or B <> {<%>E} by TARSKI:def 1;
  hence thesis by FLANG_1:14;
end;
