$. We claim that $G^{{\ifm {{\sf wt}} {{$\sf wt$}}}_r}$ and $\mathcal{R}^{{\ifm {{\sf wt}} {{$\sf wt$}}}_r}$ form a regular sequence in ${\overline{{\mathbb F}}_{\hskip-0.0mm q}}(A_{r-0},\ldots,A_0)[A_r,A_0]$. 