theorem Th60:
  P * FSeq is FinSequence of REAL
proof
  dom (P * FSeq) = dom FSeq by Th59;
  then ex n being Nat st dom (P * FSeq) = Seg n by FINSEQ_1:def 2;
  then reconsider RSeq = P * FSeq as FinSequence by FINSEQ_1:def 2;
  rng (P * FSeq) c= REAL;
  then rng RSeq c= REAL;
  hence thesis by FINSEQ_1:def 4;
end;
