theorem Th32:
  (Newton_Coeff n).(n+1) = 1
  proof
    A1: len (Newton_Coeff n) = n+1 by NEWTON:def 5; then
    A2: n = len(Newton_Coeff n) - 1;
    n+1 in dom (Newton_Coeff n) by A1,Th3; then
    (Newton_Coeff n).(n+1) = n choose n by A2,NEWTON:def 5;
    hence thesis by NEWTON:21;
  end;
