reserve a,b,i,j,k,l,m,n for Nat;

theorem
  for a be Real holds
    Sum ((a,a) Subnomial n) = Sum((1,1) Subnomial n)*Sum ((a,0)In_Power n)
proof
  let a be Real;
  Sum((1,1) Subnomial n)*Sum ((a,0)In_Power (n+1-1)) = (n+1)*(a+0)|^n
    by NEWTON:30;
  hence thesis by SAA;
end;
