%%% Cascaded items for math mode
%% start with \begin{cascade}
%% new line at previous indentation with \cascline
%% new line with greater indentation with \cascitem
%% end with \end{cascade}
%% default indentation is 2em, adjust with \cascadeindent
\newdimen\cascadeindent
\cascadeindent=1em\newdimen\cascdimen
\newcommand{\cascindent}{\global\advance\cascdimen by\cascadeindent \hspace{\cascdimen}}
\newcommand{\cascitem}{\\ \global\advance\cascdimen by\cascadeindent \hspace{\cascdimen}}
\newcommand{\cascback}[1]{\\ \global\advance\cascdimen by-#1.0\cascadeindent \hspace{\cascdimen}}
\newcommand{\cascline}{\\ \hspace{\cascdimen}}
\newenvironment{cascade}{\begin{array}[t]{@{}l@{}} \global\cascdimen=0em}{\end{array}}


%%% Binding colon stuff
\mathchardef\col="003A  % \col for binding colon (mathcode ordinary: less space)
\mathchardef\semi="603B % \semi for (regular) semicolon
%% use \semicolonforbindingcolon to redefine ; to stand for binding colon
\newcommand{\semicolonforbindingcolon}{\mathcode`;="003A}

%%% Angle bracket stuff
\mathchardef\lt="313C  % \lt for <
\mathchardef\gt="313E  % \gt for >
%% use \ltgtforanglebrackets to redefine <,> to stand for \langle, \rangle
\newcommand{\ltgtforanglebrackets}{\mathcode`<="4268 \mathcode`>="5269}

\newcommand{\kwop}[1]{\ensuremath{\mathop{\mathbf{#1}}}}
\newcommand{\kwbin}[1]{\ensuremath{\mathbin{\mathbf{#1}}}}
\newcommand{\kw}[1]{\ensuremath{\mathord{\mathbf{#1}}}}

\newcommand{\comment}[1]{\hfill \fbox{\Large{#1}}}

%\newcommand{\qed}{\rule{5pt}{8pt}} 
\newcommand{\thmbox}
   {{\ \hfill\hbox{%
      \vrule width1.0ex height1.0ex
   }\parfillskip 0pt}}

\newenvironment{proof}{{\textbf{Proof:} }}{\thmbox}
\newenvironment{proofsketch}{{\textbf{Proof (Sketch):} }}{\thmbox}

\newcommand{\thmstep}[2]{
  \noindent\begin{tabular}{@{}l@{}l}
    \lefteqn{\mbox{#1}} &\\
    \mbox{  } & $\begin{array}{l}#2\end{array}$
  \end{tabular}
  }

\newcommand{\thmstepp}[2]{
  \noindent\begin{tabular}{lll}
    \lefteqn{\mbox{#1}} &\\
    \mbox{  } & #2
  \end{tabular}
  }

\newcommand{\ifthenthm}[2]{
  \noindent\begin{tabular}[t]{@{}l@{}l}
    If & \\
    & $\begin{array}[t]{l}#1\end{array}$ \\
    then & \\
    & $\begin{array}[t]{l}#2\end{array}$
  \end{tabular}
  }

% symbol abbreviations
\newcommand{\stepsto}{\longmapsto}