theorem Th28:
  D = Seg i implies for p being FinSequence for q being
  FinSequence of D st i <= len p holds p*q is FinSequence
proof
  assume
A1: D = Seg i;
  let p be FinSequence;
  let q be FinSequence of D;
  assume i <= len p;
  then Seg i c= Seg len p by FINSEQ_1:5;
  then
A2: Seg i c= dom p by FINSEQ_1:def 3;
  rng q c= Seg i by A1,FINSEQ_1:def 4;
  then dom (p*q) = dom q by A2,RELAT_1:27,XBOOLE_1:1;
  then dom (p*q) = Seg len q by FINSEQ_1:def 3;
  hence thesis by FINSEQ_1:def 2;
end;
