
theorem Th9:
  for f,g being FinSequence holds smid(f^g,len f+1,len f+len g)=g
proof
  let f,g be FinSequence;
  len g+len f+1-'(len f+1) =len g+(len f+1)-'(len f+1) .= len g by NAT_D:34;
  then g|(len g+len f+1-'(len f+1))=g by FINSEQ_1:58;
  then ((f^g)/^(len f))|(len f+len g+1-'(len f+1))=g by FINSEQ_5:37;
  hence thesis by NAT_D:34;
end;
