Remove erroneous argument

Thanks to prime235711
https://stacks.math.columbia.edu/tag/09HK#comment-6526

fields.tex

@@ -1757,12 +1757,7 @@ \section{Purely inseparable extensions}
 for $\sigma$ we obtain the result.
 
 \medskip\noindent
-If the extensions are infinite one can write $K$ as the union
-of all finite subextension $F \subset K' \subset K$. For each
-$K'$ we set $E' = E \cap K'$. Then we have the formulas of the
-lemma for $K'/E'/F$ by the first paragraph. Since
-$[K : F]_s = \sup \{[K' : F]_s\}$ and similarly for the other
-degrees (some details omitted) we obtain the result in general.
+We omit the proof if the extensions are infinite.
 \end{proof}