Let $p\in B$ be a $K$ valued point of $B$ which is not in the image of $V(g)$. This is possible to choose since $f$ is a finite map. By going-up lemma, there exists a point $q\in X'$ lying over $p$. Let the residue field extension $[K(q):K(p)]$ be $s$. Then $s\leq$ deg $f \leq d$. Taking $L$ to be $K(q)$, we get the lemma.

[\[quantification\]]{} Let $V$ be a vector space of dimension $n$ defined over a field $K$ of char $p>0$. Let $G=SL(V)$. Let $K$ be an arbitrary field of char $p>0$. Let $\rho: Sl(V) \rightarrow Sl(V^{\otimes m})$ be the tensor power representation of $SL(n)$. Then for any non-semistable $K$-rational point $v \in
V^{\otimes m}$, the instability parabolic $P(v)$ is defined over an extension field of $[L:K]$ of degree $\leq
mn^m$. Equivalently if $t$ is such that $p^t > mn^m$, then the instability parabolic for unstable $K$-rational point is defined over $K^{1/{p^t}}$.

Let $X_1,...,X_n$ be a basis of $V$ over $K$. By uniqueness of instability parabolic and Galois descent, we may assume that all the objects are defined over the seperable closure $K_s$ of $K$. Hence without loss of generality we may assume $K=K_s$. Let $R=K\langle X_1,..,X_n \rangle$ denote 