
theorem Th39:
  for L being non empty ZeroStr,p being Polynomial of L holds
  poly_shift(p,0) = p
proof
  let L be non empty ZeroStr, p be Polynomial of L;
  set ps = poly_shift(p,0);
  now
    let x be object;
    assume x in NAT;
    then reconsider i = x as Element of NAT;
    thus ps.x = p.(0 qua Nat+i) by Def5
      .= p.x;
  end;
  hence thesis by FUNCT_2:12;
end;
