reserve a,b,c,d,m,x,n,j,k,l for Nat,
  t,u,v,z for Integer,
  f,F for FinSequence of NAT;
reserve p,q,r,s for real number;
reserve a,b,c,d,m,x,n,k,l for Nat,
  t,z for Integer,
  f,F,G for FinSequence of REAL;
reserve q,r,s for real number;
reserve D for set;

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;
