\def\frontmatter{}
\def\endfrontmatter{}

\def\keyword{\noindent Keywords:}
\def\endkeyworks{}

\makeatletter
\newdimen\@bls                              % Several dimensions are
\@bls=\baselineskip                         % expressed in terms of this.
\newenvironment{pf}%
  {\par\addvspace{\@bls \@plus 0.5\@bls \@minus 0.1\@bls}\noindent
   {\bfseries\Elproofname}\enspace\ignorespaces}%
  {\par\addvspace{\@bls \@plus 0.5\@bls \@minus 0.1\@bls}}
\def\Elproofname{PROOF.}
\@namedef{pf*}#1{\par\begingroup\def\Elproofname{#1}\pf\endgroup\ignorespaces}
\expandafter\let\csname endpf*\endcsname=\endpf
\def\qed{\relax\ifmmode\hskip2em \qedbox\else\unskip\nobreak\hskip1em $\qedbox$\fi}
\makeatother
\newcommand{\qedbox}{\ \hfill\rule{1.5ex}{1.5ex}\vspace{\smallskipamount}}

\newtheorem{thm}{Theorem}
\newtheorem{cor}[thm]{Corollary}
\newtheorem{lem}[thm]{Lemma}
\newtheorem{claim}[thm]{Claim}
\newtheorem{axiom}[thm]{Axiom}
\newtheorem{conj}[thm]{Conjecture}
\newtheorem{fact}[thm]{Fact}
\newtheorem{hypo}[thm]{Hypothesis}
\newtheorem{assum}[thm]{Assumption}
\newtheorem{prop}[thm]{Proposition}
\newtheorem{crit}[thm]{Criterion}
\newtheorem{defn}[thm]{Definition}
\newtheorem{exmp}[thm]{Example}
\newtheorem{rem}[thm]{Remark}
\newtheorem{prob}[thm]{Problem}
\newtheorem{prin}[thm]{Principle}
\newtheorem{alg}{Algorithm}

\newcommand{\half}{\frac{1}{2}}

\def\etal{et al.}
