
theorem Th56:
  for L be commutative associative well-unital distributive
  almost_left_invertible non empty doubleLoopStr for p be Polynomial of L st
  len p <> 0 holds (NormPolynomial p).(len p-'1) = 1.L
proof
  let L be commutative associative well-unital distributive
  almost_left_invertible non empty doubleLoopStr;
  let p be Polynomial of L;
  assume len p <> 0;
  then len p >= 0+1 by NAT_1:13;
  then len p = len p-'1+1 by XREAL_1:235;
  then
A1: p.(len p-'1) <> 0.L by ALGSEQ_1:10;
  thus (NormPolynomial p).(len p-'1) = p.(len p-'1) / p.(len p-'1) by Def11
    .= p.(len p-'1) * (p.(len p-'1))"
    .= 1.L by A1,VECTSP_1:def 10;
end;
