theorem Th17:
  for f1 being FinSequence st len f1<k holds mid(f1,k,k)={}
proof
  let f1 be FinSequence;
  assume
A1: len f1<k;
  then len f1+1<=k by NAT_1:13;
  then
A2: len f1+1-1<=k-1 by XREAL_1:9;
  0+1<=k by A1,NAT_1:13;
  then len f1<=k-'1 by A2,XREAL_1:233;
  then
A3: f1/^(k-'1)={} by FINSEQ_5:32;
  k-'k+1=k-k+1 by XREAL_1:233
    .=1;
  then mid(f1,k,k)=(f1/^(k-'1))|1 by Def3;
  hence thesis by A3;
end;
