
theorem NC4:
  Newton_Coeff 4 = <*1,4,6,4,1*>
  proof
    A1: <*0*>^<*1,3,3,1*> = <*0,1,3,3,1*> & <*1,3,3,1*>^<*0*> = <*1,3,3,1,0*>
      by FINSEQ_4:75;
    Newton_Coeff (3 + 1) = <*0,1,3,3,1*> + <*1,3,3,1,0*> by A1,PT,NC3
    .= <*0+1,1+3,3+3,3+1,1+0*> by A5B5;
    hence thesis;
  end;
