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Using the memoir class and the cleveref package as in the MWE included below, I would like to have as name of a sectional division marked with \section after the \appendix declaration, the same name as before: "section". Nonetheless, what I get is "appendix". Any hints as to how to obtain the desired behavior will be welcome.

\documentclass{memoir}

\usepackage{cleveref} 

\begin{document}
\chapter{First Chap.}\label{firstch}
This is some intro with a reference to \cref{firstch}.
\section{First Chap. Section}\label{firstchapsec}
And now a reference to \cref{firstchapsec}. This is fine; I want the name "section".
\appendix  
\chapter{First App.}\label{firstapp}
This is the app. with a reference to \cref{firstapp}.
\section{First App. Section}\label{firstappsec}
And now a reference to \cref{firstappsec}. I want to have "section" instead of "appendix".
\end{document}
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    As this also happens with the standard book class, this is not memoir related. – daleif Nov 16 '17 at 13:55
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    Good to know. Just in case that someone comes up with a memoir-specific answer, I'll leave the tags and the title as they are. If the answer is memoir-independent I'll delete the memoir tag and rephrase the title. – Marcos Nov 16 '17 at 13:59
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To change from appendix A.1 to section A.1 you can use the following line in the preamble of your document:

\crefname{subappendix}{section}{sections}

Analogously, you can also change appendix A to chapter A and appendix A.1.1 to subsection A.1.1 with the following lines:

\crefname{appendix}{chapter}{chapters}
\crefname{subsubappendix}{subsection}{subsections}

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