reserve x, x1, x2, y, X, D for set,
  i, j, k, l, m, n, N for Nat,
  p, q for XFinSequence of NAT,
  q9 for XFinSequence,
  pd, qd for XFinSequence of D;

theorem Th1:
  ex qd st pd = (pd|n)^qd
proof
  consider q9 such that
A1: pd = (pd|n)^q9 by AFINSQ_1:60;
  rng q9 c= rng pd by A1,AFINSQ_1:25;
  then rng q9 c= D by XBOOLE_1:1;
  then q9 is XFinSequence of D by RELAT_1:def 19;
  hence thesis by A1;
end;
