rearranging the Hochschild section. Splitting things up into lemmas, and explaining why those lemmas are what we need.
\documentclass{amsart}\newcommand{\pathtotrunk}{../../}% \input{\pathtotrunk text/article_preamble.tex}\pagestyle{empty}\begin{document}\thispagestyle{empty}\begin{align*}f^{(k)} P S \dots\end{align*}\end{document}