diff --git a/elegantbook-en.tex b/elegantbook-en.tex index 376611f..120716d 100644 --- a/elegantbook-en.tex +++ b/elegantbook-en.tex @@ -14,8 +14,6 @@ \logo{logo-blue.png} \cover{cover.jpg} -\providecommand\qed{} -\renewcommand{\qed}{\hfill\ensuremath{\square}} \begin{document} @@ -642,7 +640,7 @@ \section{Writing Sample} \end{proposition} \begin{proof} -Let $z$ be some element of $xH \cap yH$. Then $z = xa$ for some $a \in H$, and $z = yb$ for some $b \in H$. If $h$ is any element of $H$ then $ah \in H$ and $a^{-1}h \in H$, since $H$ is a subgroup of $G$. But $zh = x(ah)$ and $xh = z(a^{-1}h)$ for all $h \in H$. Therefore $zH \subset xH$ and $xH \subset zH$, and thus $xH = zH$. Similarly $yH = zH$, and thus $xH = yH$, as required. \qed +Let $z$ be some element of $xH \cap yH$. Then $z = xa$ for some $a \in H$, and $z = yb$ for some $b \in H$. If $h$ is any element of $H$ then $ah \in H$ and $a^{-1}h \in H$, since $H$ is a subgroup of $G$. But $zh = x(ah)$ and $xh = z(a^{-1}h)$ for all $h \in H$. Therefore $zH \subset xH$ and $xH \subset zH$, and thus $xH = zH$. Similarly $yH = zH$, and thus $xH = yH$, as required. \end{proof} \begin{figure}[htbp] diff --git a/elegantbook.cls b/elegantbook.cls index 210e742..babdc6e 100644 --- a/elegantbook.cls +++ b/elegantbook.cls @@ -8,7 +8,7 @@ %%%%%%%%%%%%%%%%%%%%% % % !Mode:: "TeX:UTF-8" \NeedsTeXFormat{LaTeX2e} -\ProvidesClass{elegantbook}[2020/02/10 v3.10 ElegantBook document class] +\ProvidesClass{elegantbook}[2020/04/11 v4.0.0 ElegantBook document class] \RequirePackage{kvoptions} \RequirePackage{etoolbox}