theorem Th1:
  for f be FinSequence holds
    f is D-valued iff f is FinSequence of D
  proof
    let f be FinSequence;
    f is D-valued implies f is FinSequence of D
    proof
      assume f is D-valued; then
      rng f c= D by RELAT_1:def 19;
      hence thesis by FINSEQ_1:def 4;
    end;
    hence thesis;
  end;
