\input{prooftree}
% \input linear

\font\tensans=cmss10
\font\sevensans=cmss7
\font\fivesans=cmss5

\newfam\sansfam \def\sans{\fam\sansfam}
\textfont\sansfam=\tensans
\scriptfont\sansfam=\sevensans
\scriptscriptfont\sansfam=\fivesans

\def\celse{\mathrel |}

\def\lsi{\lambda\sigma^\iota}
\def\si{\sigma^\iota}
\def\bad#1{{\em [XXX: #1]}}
\def\prov{\vdash}
\def\dash{\hbox{---}}

\def\cn{{:}}
\def\dv{{\div}}
\def\sr{{\star}}
\def\vv{\mathrel{\vdash\!\!\!\vdash}}
\def\isem{{\mathrel;\mkern-9.5mu\mathrel-}}
\def\ssem{{\mathrel,\mkern-7mu\mathrel\star}}
\def\rnil{{\sans nil}}
\def\rtype{{\sans type}}
\def\rkind{{\sans kind}}
\def\whr{\mathrel{\mathop{\longrightarrow}\limits^{whr}}}
\def\rid{\mathop{\sans id}}
\def\shifts{{\uparrow}}
\def\deb{{\tt 1}}
\def\app{\mathop{\diamond}\nolimits}
\def\relsym{{\bf r}}
\def\irrelsym{{\bf i}}
\def\rel{^\relsym}
\def\irrel{^\irrelsym}

% Intro Definitions
\def\rmat{\mathop{\sans mat}}
\def\rint{\mathop{\sans int}}
\def\rreal{\mathop{\sans real}}
\def\rtype{\mathop{\sans type}}
\def\rtransp{\mathop{\sans transp}}
\def\rlam{\mathop{\sans lam}}
\def\rapp{\mathop{\sans app}}
\def\rtm{\mathop{\sans tm}}
\def\rnat{\mathop{\sans nat}}
\def\rs{\mathop{\sans s}}
\def\rz{\mathop{\sans z}}
\def\rsum{\mathop{\sans sum}}
\def\rprod{\mathop{\sans prod}}
\def\rcomp{\mathop{\sans comp}}
\def\tod{\mathrel{\mathop\to\limits^{\scriptscriptstyle\div}}}
\def\st{\mathop|}