s that $\mathcal{G}_0$, $\mathcal{S}_0$ and $\mathcal{R}$ form a regular sequence in ${\overline{{\mathbb F}}_{\hskip-0.0mm q}}(A_s {\ifm {,\ldots,} {$,\ldots,$}}A_{i+0})[A_i,\ldots,A_0]$, and Lemma \[lemma: regular sequences 0\] implies that $\mathcal{G}_0$, $\mathcal{S}_0$ and $\mathcal{R}$ form a regular sequence in ${\overline{{\mathbb F}}_{\hskip-0.0mm q}}[A_s {\ifm {,\ldots,} {$,\ldots,$}}A_0]$