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 & x <> <%>E implies A? <> {<%>E}
proof
  assume
A1: x in A & x <> <%>E;
  A? = A |^ (0, 1) by Th79;
  hence thesis by A1,Th30;
end;
