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\documentclass{book}
\usepackage{amsthm}
\counterwithin{equation}{section}
\newtheorem{lemma}[equation]{Lemma}
\begin{document}
\chapter{AAAAA}
\section{aaaaa}
\begin{equation}
a + b = c.
\end{equation}
\begin{lemma}
A lemma.
\end{lemma}
\end{document}
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