
theorem NC3:
  Newton_Coeff 3 = <*1,3,3,1*>
  proof
    reconsider f = <*1,3,3*> as 3-element real-valued FinSequence;
    len (Newton_Coeff 3) = 3 + 1 by NEWTON:def 5; then
    dom (Newton_Coeff 3) = Seg 4 & (Newton_Coeff 3).1 = 1 &
      (Newton_Coeff 3).(3+1) = 1 & (Newton_Coeff 3).2 = 3 &
        (Newton_Coeff 3).3 = 3 by FINSEQ_1:def 3;
    hence thesis;
  end;
