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 Th11:
  for P, p, q, m, n st p in P^^m & q in P^^n holds p^q in P^^(m+n)
proof
  let P, p, q, m, n;
  assume p in P^^m & q in P^^n;
  then p^q in (P^^m)^(P^^n) by Def2;
  hence thesis by Th10;
end;
