
theorem
  for k be Nat,
  c be XFinSequence of REAL
  st len c = k+1 & 0 < c.k holds seq_p(c) is polynomially-bounded
  proof
    let k be Nat,
    c be XFinSequence of REAL;
    assume AS: len c = k+1 & 0 < c.k;
    take k;
    thus thesis by LMXFIN20A,TLNEG3,AS;
  end;
