\documentclass[10pt]{beamer}
\input mybeamer.sty
%\input thmsty.sty
\input epsf.sty
\usepackage{epic,eepic}
\usepackage{graphics,color}
%\pagestyle{empty}
%\oddsidemargin 0pt
%\textwidth 6.5in
%\textheight 9.5in
%\topmargin -.5in
\usepackage{multicol}
\newenvironment{checkenv}{\only{\setbeamertemplate{enumerate item}{\red{$\checkmark$}}}}{}
\title{$A_n$ is simple}

\author{}
\date{}
\begin{document}

%\begin{frame}
%\titlepage
%\frametitle{}

\begin{frame}\frametitle{Strategy ($A_n$ is simple)}

\bt If $n\ne 4,$ then $A_n$ is simple.
\et

\be
\visible<2->{\item<beamer:check@8-> We may assume $n\ge 5.$}
\visible<3->{\item<beamer:check@9-> Take $N\trianglelefteq A_4,$ $N\ne <(1)>.$}
\visible<4->{\item<beamer:check@10-> Three cases for cycles appearing in elements of $N$:}
\visible<5->{\item<beamer:check@11-> Case 1: Some cycle has length 4.  Construct a 3-cycle in $N$.}
\visible<6->{\item<beamer:check@12-> Case 2: Some cycle has length 3 but none are longer.  Construct a 5-cycle or a 3-cycle in $N$.} 
\visible<7->{\item<beamer:check@13-> Case 3: All cycles have length at most 2. Construct a 3-cycle in $N.$}
%\visible<8->{\item<beamer:check@15->}
\ee



\end{frame}

\end{document}
