answer.tex

\documentclass[]{book}
\usepackage{proof}
\usepackage{epic}
\usepackage{eepic}
\textheight 100cm
\textwidth 100cm
\newcommand{\Poss}[1]   {\mbox{$\langle${#1}$\rangle$}}
\newcommand{\Bx}[1]     {\mbox{$[${#1}$]$}}
\newcommand{\AND}       {\mbox{$\bigwedge$}}
\newcommand{\OR}        {\mbox{$\bigvee$}}
\begin{document}
\pagestyle{empty}
\infer[\mbox{R-\OR}]{\Poss{a}T\OR \Poss{b}\Poss{c}T \vdash \Poss{a}T\OR \Poss{b}T}{
\infer[\mbox{L-\OR}]{\Poss{a}T\OR \Poss{b}\Poss{c}T \vdash \Poss{a}T,\Poss{b}T}{
\infer[\mbox{weak}]{\Poss{a}T \vdash \Poss{a}T,\Poss{b}T}{
\infer[\mbox{poss}]{\Poss{a}T \vdash \Poss{a}T}{
\infer[\mbox{\cal T}]{T \vdash T}{
}
}
}
 & \infer[\mbox{weak}]{\Poss{b}\Poss{c}T \vdash \Poss{a}T,\Poss{b}T}{
\infer[\mbox{poss}]{\Poss{b}\Poss{c}T \vdash \Poss{b}T}{
\infer[\mbox{\cal T}]{\Poss{c}T \vdash T}{
}
}
}
}
}

 \section*{A nice Proof}
\end{document}