%\documentclass[a4paper,12pt,draft]{amsart}% English
\documentclass[a4paper,12pt]{jsarticle} %日本語
\usepackage{amsmath, amssymb, amsthm}
\usepackage{braket}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% theorems 日本語/English

\theoremstyle{definition}  %% 日本語
% \theoremstyle{plain}   %% English

\newtheorem{thm}{Theorem}[section]
\newtheorem{theorem}[thm]{Theorem}
\newtheorem{lemma}[thm]{Lemma}
\newtheorem{corollary}[thm]{Corollary}
\newtheorem{cor}[thm]{Corollary}
\newtheorem{proposition}[thm]{Proposition}
\newtheorem{prop}[thm]{Proposition}

\theoremstyle{definition}  %% 日本語
%\theoremstyle{remark}  %% English

\newtheorem{remark}[thm]{Remark}
\newtheorem{rem}[thm]{Remark}
\newtheorem{example}[thm]{Example}
\newtheorem{exercise}[thm]{Exercise}

\newtheorem*{acknowledgment}{Acknowledgment}
\newtheorem*{ackn}{Acknowledgment}

\theoremstyle{definition}  %% 日本語
%\theoremstyle{definition}  %% English
\newtheorem{definition}[thm]{Definition}
\newtheorem{dfn}[thm]{Definition}
\newtheorem{algorithm}[thm]{Algorithm}
\newtheorem{question}[thm]{Question}
\newtheorem{problem}[thm]{Problem}
\newtheorem{notation}[thm]{Notation}
\newtheorem{conjecture}[thm]{Conjecture}
\newtheorem{conj}[thm]{Conjecture}

% theorems 日本語/English
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% blackboard bold capital

\newcommand{\ZZ}{\mathbb{Z}}
\newcommand{\CC}{\mathbb{C}}
\newcommand{\NN}{\mathbb{N}}
\newcommand{\RR}{\mathbb{R}}
\newcommand{\QQ}{\mathbb{Q}}
\newcommand{\EE}{\mathbb{E}}

% blackboard bold capital
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% caligraphic capital

\newcommand{\AAA}{\mathcal{A}}
\newcommand{\BBB}{\mathcal{B}}
\newcommand{\CCC}{\mathcal{C}}
\newcommand{\FFF}{\mathcal{F}}
\newcommand{\TTT}{\mathcal{T}}
\newcommand{\HHH}{\mathcal{H}}

% caligraphic capital
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% bold italic

\newcommand{\xx}{\boldsymbol{x}}
\newcommand{\yy}{\boldsymbol{y}}
\newcommand{\zz}{\boldsymbol{z}}

\newcommand{\aalpha}{\boldsymbol{\alpha}}
\newcommand{\bbeta}{\boldsymbol{\beta}}

% bold italic
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% commands like  \det

\newcommand{\End}{\operatorname{End}}
\newcommand{\len}{\operatorname{len}}
\newcommand{\tr}{\operatorname{tr}}
\newcommand{\codim}{\operatorname{codim}}
\newcommand{\prob}{\operatorname{Pr}}
\newcommand{\diag}{\operatorname{diag}}
\newcommand{\sgn}{\operatorname{sgn}}

% commands like  \det
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% independent 
\makeatletter
\DeclareSymbolFont{symbolsC}{U}{txsyc}{m}{n}
\DeclareMathSymbol{\MYPerp}{\mathrel}{symbolsC}{121}
\makeatother
\newcommand{\indep}{\MYPerp}
% independent 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% misc (command)

\newcommand{\der}{\partial}

% misc (command)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% misc (setting)

\allowdisplaybreaks[3] %denine 0-4 allow

% misc (setting)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\begin{document}

\title{}
\author{}
\date{}
\maketitle

\section{Example}

\begin{theorem}
\label{thm:1}
A therem
\end{theorem}
\begin{proof}
This is a proof of \ref{thm:1}.
\end{proof}


\begin{theorem}[Name]
Another therem
\end{theorem}


\begin{lemma}
A therem
\end{lemma}

\begin{cor}
A corollary
\end{cor}

\begin{prop}
A proposition
\end{prop}

\begin{example}
An example
\end{example}

\begin{ackn}
An acknoledgement
\end{ackn}

\begin{align*}
& A \indep  B \\
& \NN \ZZ \QQ \RR \CC \EE \\
& \AAA \BBB \\
& \aalpha \bbeta \\
& \xx \yy \zz \\
& \text{数式中の文. A text in math mode} \\
& \prob \tr \len \codim  \sgn \diag \\
\der A&= \binom{2}{3}\\
\Set{ a \in \ZZ |  \frac{a}{2}\in \ZZ }
&= \Set{ a \in \ZZ |  \text{$a$は偶数} }\\
\end{align*}

\end{document}