
\newcommand\derl{\texttt{derl}}
\newcommand\derrec{\texttt{derrec}}
\newcommand\rls{\texttt{rls}}
\newcommand\adm{\texttt{adm}}

\newcommand\invrule[2]{ 
% for use in non-math mode, args interpreted in math mode
  \begin{tabular}{@{}c@{}}
  $ #1 $ \\ \hline \hline $ #2 $
  \end{tabular}}
\newcommand\slrule[2]{ % similar to \frac, except
% for use in non-math mode, args interpreted in math mode
  \begin{tabular}{@{}c@{}}
  $ #1 $ \\ \hline $ #2 $
  \end{tabular}}

\newcommand\src[1]{source file \texttt{#1}}
\newcommand\apsrc[1]{Appendix \ref{app:code}}
\newcommand\seesrc[1]{(see source file \texttt{#1})}
\newcommand\insrc[1]{in source file \texttt{#1}}
\newcommand\page[1]{page~\pageref{#1}}
\newcommand\fig[1]{Fig.~\ref{fig:#1}}
\newcommand\ch[1]{Chapter~\ref{ch:#1}}
\newcommand\tbl[1]{Table~\ref{tbl:#1}}
\newcommand\thrm[1]{Theorem~\ref{thrm:#1}}
\newcommand\lem[1]{Lemma~\ref{lem:#1}}
\newcommand\ttl[1]{\tti{#1}\label{#1}}
\newcommand\ttdl[1]{\texttt{#1}\tti{#1}\label{#1}}
\newcommand\ttdef[1]{\texttt{#1}\tti{#1}}
\newcommand\tti[1]{\index{#1@\texttt{#1}}}
\newcommand\bfi[1]{\textbf{#1}\index{#1|textbf}}
\newcommand\dRA{{\boldmath $\delta$}\textbf{RA}}
\newcommand\dKt{{\boldmath $\delta$}\textbf{Kt}}
\newcommand\NRA{\textbf{NRA}}
\newcommand\RA{\textbf{RA}}
%\newcommand\M{$\mathcal M$}
\newcommand\MP{\ensuremath{\mathcal P}}
\newcommand\MQ{\ensuremath{\mathcal P}}
\newcommand\MR{\ensuremath{\mathcal C}}
\newcommand\M{\ensuremath{\mathcal M}}
\newcommand\Mp{$\mathcal M'$}
\newcommand\up[1]{\vspace{-#1ex}} 
\newcommand\vpf{\vspace{-3ex}} % to reduce space before proof tree
\newcommand\1{\textbf 1}
\newcommand\0{\textbf 0}
\newcommand\cut{(\emph{cut})}
\newcommand\dt{\texttt{dt}}
\newcommand\dtn{\texttt{dtn}}

\newcommand{\pordered}[3]{#1 <_{\texttt{\scriptsize #2}} #3}
\newcommand{\Revpordered}[3]{#1 >_{\texttt{\scriptsize #2}} #3}
\newcommand{\LRPord}[2]{\pordered{#1}{LRP}{#2}}
\newcommand{\cutord}[2]{\pordered{#1}{cut}{#2}}
\newcommand{\snoneord}[2]{\pordered{#1}{sn1}{#2}}
\newcommand{\dtord}[2]{\pordered{#1}{dt}{#2}}
\newcommand{\Revdtord}[2]{\Revpordered{#1}{dt}{#2}}

\newcommand\GL{\textbf{GL}}
\newcommand\GLS{\textrm{GLS}}
\newcommand\GLR{\textit{GLR}}
\newcommand\GLRp{\ensuremath{\Box X, X, \Box B \vdash B}} % premise of GLR
\newcommand\GLRc{\ensuremath{\Box X \vdash \Box B}} % conclusion of GLR
\newcommand\lxxc{\ensuremath{\Box X, X \vdash B}} % conclusion of lem20
\newcommand\gbna{\ensuremath{\Box G, \Box B^k \vdash \Box A}} 
\newcommand\GLRB{\textit{GLR}($B$)}
\newcommand\GLRXB{\textit{GLR}($X,B$)}

\newcommand\pmz{\texttt{pm0}}
\newcommand\pmgez{\texttt{pm\_ge0}}

\newcommand\delz{\texttt{del0}}
\newcommand\delzs{\ensuremath{\partial^0}}

\newcommand\muxbn{\texttt{muxbn}}

