Proof
We have just to apply lemma 3.4
\(F_{1}(S_{1}=0,S_{2}\geq 0,\ldots{,S}_{n-1}\geq 0)=0\geq 0,\)
\(F_{2}\left(S_{1}\geq 0,S_{2}=0,\ldots{,S}_{n-1}\geq 0\right)=2\left(1-a_{1}\right)p_{1}S_{1}\geq 0,\ \ since\ \ a_{1}\leq 1\)
\(\vdots\)
\begin{equation} F_{n-1}\left(S_{1}\geq 0,\ldots{,S}_{n-1}=0\right)=2\left(1-a_{n-2}\right)p_{n-2}S_{n-2}\geq 0,\ \ since\ \ a_{n-2}\leq 1\nonumber \\ \end{equation}\begin{equation} \begin{matrix}G_{1}\left(S\geq 0,\ T=0,T_{i}\geq 0,\ \ V\geq 0\right)=\lambda+2\left(1-a_{n-1}\right)p_{n-1}S_{n-1}\geq 0,\ since\ \ a_{n-1}\leq 1\\ G_{2}\left(S\geq 0,\ T\geq 0,T_{i}=0,\ \ V\geq 0\right)=\text{kTV}\geq 0\\ G_{3}\left(S\geq 0,\ T\geq 0,T_{i}\geq 0,\ V=0\right)=\sigma T_{i}\geq 0\\ \end{matrix}\nonumber \\ \end{equation}