\documentclass[twoside,a4paper]{amsart}

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\setlength{\textwidth}{120mm}
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\usepackage[english]{babel}
\thispagestyle{empty}
\usepackage{amssymb}
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\usepackage{amsmath}
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\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{definition}{Definition}[section]
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{remark}{Remark}[section]
\newtheorem{remarks}[remark]{Remarks}
\newtheorem{example}{Example}[section]
\newtheorem{examples}[example]{Examples}
\def\proof{\trivlist \item[\hskip \labelsep{\sc Proof.}]}
\def\endproof{\hfill $\square$
\endtrivlist}


\def\proofofT{\trivlist \item[\hskip \labelsep{\sc Proof of Theorem}]}
\def\endproofofT{\hfill $\square$
\endtrivlist}

\def\proofofC{\trivlist \item[\hskip \labelsep{\sc Proof of Corollary}]}
\def\endproofofC{\hfill $\square$
\endtrivlist}

\def\theequation{\thesection.\arabic{equation}}
\setcounter{section}{0}
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%\hspace*{0.7cm}%

%%%%%%%%%%%%%%%%%%%%Editor definitions. Please do not change!

\usepackage{color}

%%%%%%%%%%Author definitions. Please change here!!!



%%%%%%%%%%%%%%%%%%%%%%%%

 \author{Insert name of Author}
 \address{Insert Address}
 \email{Insert e-mail}
\title[Short title]{Title}
 \dedicatory{Dedicated to ....}
 \subjclass[2010]{ ... }
 \keywords{ ....}

\thanks{The work was supported by ...}

 \def\labelauthor{InitialsOfAuthor} %%%INSERT Initials
 
\begin{document}

\begin{abstract}
An abstract

\end{abstract}

\maketitle

%------------- BEGINNING OF THE BODY OF THE ARTICLE -----------------%%



%% --- Each section begins with --- %%
\section{Introduction}\label{Introduction}
\setcounter{equation}{0}


%% -- The propositions, theorems, definitions, corollaries etc...
%%     are defined as follows ---%%

\begin{definition}\label{\labelauthor:defi:label}%% replace  label 
WRITE HERE THE Definition
\end{definition}

\begin{remark}\label{\labelauthor:rem:label}%% replace  label 
WRITE HERE THE Remark
\end{remark}

\begin{example}\label{\labelauthor:ex:label}%% replace  label 
WRITE HERE THE Example
\end{example}

\begin{proposition}\label{\labelauthor:pro:label}%% replace  label 

WRITE HERE THE proposition
\end{proposition}

\begin{lemma}

WRITE HERE THE Lemma
\end{lemma}

\begin{theorem}\label{\labelauthor:teo:label}%% replace  label 
%{lemma} for a lemma; {corollary} for a corollary;
%{definition} for a definition; {proposition} for a proposition;
%{remark} for a remark; {remarkss} for remarks; {example} for an example;
%{examples} for examples; {proof} for proof.
WRITE HERE THE THEOREM
\end{theorem}
\begin{proof}
Here are some equations

\begin{equation}\label{\labelauthor:eq:label1}\\ %% replace  label 
S=\sum_{i=1}^{n}\frac{1}{i^2}
\end{equation}

\begin{eqnarray}
b(x)&=&\int_x^1f(s)\frac{ds}{s}\label{\labelauthor:eqn:label1}\\ %% replace  label 1
&\approx&g(x),\qquad x\in(0,\frac{1}{2}).\nonumber
\end{eqnarray}
\end{proof}

\

\begin{corollary}\label{\labelauthor:cor:label}%% replace  label 
WRITE HERE THE Corollary
\end{corollary}


Text and comments .... The proof of previous corollary will be given later on! 

Text .......

\begin{proofofC}{\sc \ref{\labelauthor:cor:label}}. 
Here are some equations

\begin{equation}
S=\sum_{i=1}^{n}\frac{1}{i^2}
\end{equation}

\begin{eqnarray}
b(x)&=&\int_x^1f(s)\frac{ds}{s}\label{\labelauthor:eqn:label2}\\%% replace  label  2
&\approx&g(x),\qquad x\in(0,\frac{1}{2}).\nonumber
\end{eqnarray}

\end{proofofC}

\section{Section 2}

\setcounter{equation}{0}


\section*{Acknowledgments}

I kindly acknowledge....


%% ----------------------- REFERENCES -------------------------------%%

\begin{thebibliography}{99}


\bibitem{\labelauthor:bib:label}%% replace  label 
F. Tr\`eves, \textsl{Topological Vector Spaces, Distributions and
Kernels}, Academic Press, New York, 1967.
\end{thebibliography}
\end{document}


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