$\begin{align*}
0\leq v^{\tau}R^{-1}d &= 
		\begin{bmatrix} v^{\tau}_{1} & v^{\tau}_{2}\end{bmatrix}
		\begin{bmatrix} (I-\alpha H_{11})^{-1} & \alpha(I-\alpha H_{11})^{-1}H_{12}\\	0 & I \end{bmatrix} \begin{bmatrix} 0\\ e \end{bmatrix} \\
	&=\alpha v^{\tau}_{1}	(I-\alpha H_{11})^{-1}H_{12}e+v^{\tau}_{2}e \\
	&=1-(1-\alpha)v^{\tau}_{1}(I-\alpha H_{11})^{-1}e.
\end{align*}$