meow.tex

\documentclass{article}

\usepackage{mathpartir}
\usepackage{tikz}

% https://tex.stackexchange.com/questions/122415/mathchoice-and-tikzs-remember-picture
\newcommand{\tikzmark}[2]{\tikz[remember picture,inner sep=0,baseline,anchor=base] \node (#1) {#2};}

\begin{document}
\[
\inferrule
{e_1 : \Pi x:A.B \\
 \tikzmark{d}{$e_2$} : A}
{e_1 ~ \tikzmark{a}{$e_2$} : B[\tikzmark{b}{$e_2$}/x]
\tikz[overlay,remember picture] {\draw[-latex,bend left=30] (a.north) to (b.north);}
\tikz[overlay,remember picture] {\draw[thick,dotted,-latex,bend right=50] (a.south) to (d.south);}
}
\]
\end{document}