reserve i,i1,i2,i3,i4,i5,j,r,a,b,x,y for Integer,
  d,e,k,n for Nat,
  fp,fk for FinSequence of INT,
  f,f1,f2 for FinSequence of REAL,
  p for Prime;

theorem
  len fp = 1 implies for x being Element of INT holds (Poly-INT fp).x = fp.1
proof
  assume
A1: len fp = 1;
  let x be Element of INT;
  consider fr being FinSequence of INT such that
A2: len fr = len fp and
A3: for d st d in dom fr holds fr.d = (fp.d) * x|^(d-'1) and
A4: (Poly-INT fp).x = Sum fr by Def1;
  1 in dom fr by A1,A2,FINSEQ_3:25;
  then
A5: fr.1 = (fp.1) * x|^(1-'1) by A3
    .= fp.1 * x|^0 by XREAL_1:232
    .= fp.1 * 1 by NEWTON:4;
  fr = <*fr.1*> by A1,A2,FINSEQ_1:40;
  hence thesis by A4,A5,RVSUM_1:73;
end;
