b$)$ Under certain conditions, one can generalize that the Binomial Option Pricing

Model $($BOPM$)$ is complete such that:

$x_{n+1}({}_1,$cdots,${}_n$;$T)={}_n({}_1,$cdots,${}_n$;$T)S_{n+1}({}_1,$cdots,${}_n$;$T)$

$+(1+r)x_n({}_1,$cdots,${}_n$;$T)$

$-{}_n({}_1,$cdots,${}_n)S_n({}_1,$cdots,${}_n)$

Show that if the portfolio process above is well defined then:

$x_{n+1}(T)=C_{n+1}(T)$