reserve i, j, n for Element of NAT,
  f, g, h, k for FinSequence of REAL,
  M, N for non empty MetrSpace;

theorem
  for f, g being FinSequence holds dom g c= dom (f^g)
proof
  let f, g be FinSequence;
  len g <= len f + len g by NAT_1:11;
  then Seg len g c= Seg (len f + len g) by FINSEQ_1:5;
  then dom g c= Seg (len f + len g) by FINSEQ_1:def 3;
  hence thesis by FINSEQ_1:def 7;
end;
