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 Th6:
  for P holds P^^0 = {{}} & for n holds P^^(n+1) = (P^^n)^P
proof
  let P;
  thus P^^0 = {{}} by Def3;
  let n;
  consider Q such that A1: Q = P^^n & P^^(n+1) = Q^P by Def3;
  thus thesis by A1;
end;
