theorem
  D = Seg i implies for p being FinSequence of D9 for q being
  FinSequence of D st i <= len p holds p*q is FinSequence of D9
proof
  assume
A1: D = Seg i;
  let p be FinSequence of D9;
  let q be FinSequence of D;
  assume i <= len p;
  then reconsider pq = p*q as FinSequence by A1,Th28;
  rng pq c= rng p & rng p c= D9 by FINSEQ_1:def 4,RELAT_1:26;
  then rng pq c= D9;
  hence thesis by FINSEQ_1:def 4;
end;
