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 Th7:
  for P holds P^^1 = P
proof
  let P;
  thus P^^1 = P^^(0+1) .= (P^^0)^P by Th6 .= {{}}^P by Th6 .= P by Th3;
end;
