reserve k,m,n for Nat,
  a, b, c for object,
  x, y, X, Y, Z for set,
  D for non empty set;
reserve p, q, r, s, t, u, v for FinSequence;
reserve P, Q, R, P1, P2, Q1, Q2, R1, R2 for FinSequence-membered set;
reserve S, T for non empty FinSequence-membered set;

theorem Th9:
  for P holds {} in P* & P c= P*
proof
  let P;
  {} in P^^0 & P^^1 = P by Th4;
  hence thesis by Th5;
end;
