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426 lines
21 KiB
426 lines
21 KiB
% mangletex (11 May 1992) run at 22:09 GMT Monday 08 November 1993
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%%\title {\TeX\ macros for proof boxes}
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%%\author {Paul Taylor\\
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%% Department of Computing,\\
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%% Imperial College,\\
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%% London SW7 2BZ\\
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%% +44 71 589 5111 {\em ext.} 5057\\
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%% {\tt<pt@doc.ic.ac.uk>}}
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%%\date{8 November 1993}
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%% % to get the provisional user documentation do
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%% % grep ^%% boxproof.tex | sed 's/^%*//' > boxproof-manual.tex
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%%\documentstyle{article}
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%%\input boxproof.tex
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%%\def\meta#1{\mbox{$\langle\hbox{#1}\rangle$}}
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%%\def\macrowitharg#1#2{{\tt\string#1\bra\meta{#2}\ket}}
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%%{\escapechar-1 \xdef\bra{\string\{}\xdef\ket{\string\}}}
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%%\let\subsection\section
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%%\begin{document}
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%%\maketitle
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%%
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%% \subsection{Introduction}
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%% The proof
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%%\begin{proofbox}
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%% \(\"1"\:\alpha\leftrightarrow\psi(x,\top)\=\\
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%% \:\Some\beta.\psi(x,\beta)\=\mathsf{total}\\
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%% \[\exists\beta\kern-1em\:\psi(x,\beta)\\
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%% \(\:\beta\=\\
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%% \:\beta=\top\=(*)\\
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%% \:\psi(x,\!\top)\=\mathsf{subs}\\
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%% \:\alpha\=\elim\leftrightarrow(\ref{1})\\
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%% \*\:\alpha\=\\
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%% \:\psi(x,\!\top)\=\elim\leftrightarrow(\ref{1})\\
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%% \:\beta=\top\=\mathsf{func}\\
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%% \:\beta\=(*)\\
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%% \)\:\alpha=\beta\=\intro\leftrightarrow\\
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%% \:\psi(x,\alpha)\=\mathsf{subs}\\
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%% \] \:\psi(x,\alpha)\=\elim\exists\\
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%% \* \:\psi(x,\alpha)\=\\
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%% \(\:\alpha\=\\
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%% \:\alpha=\top\=(*)\\
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%% \:\phi(x,\!\top)\=\mathsf{subs}\\
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%% \*\:\psi(x,\!\top)\=\\
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%% \:\alpha=\top\=\mathsf{func}\\
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%% \:\alpha\=(*)\\
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%% \)\:\alpha\leftrightarrow\psi(x,\!\top)\=\intro\leftrightarrow\\
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%%% \) \:\psi(x,\alpha)\leftrightarrow(\alpha\leftrightarrow\psi(x,\!\top))
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%% \=\intro\leftrightarrow\\
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%%\end{proofbox}
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%% is produced by
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%%\begin{verbatim}
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%%\begin{proofbox}
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%% \(\"1"\:\alpha\leftrightarrow\psi(x,\top)\\
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%% \:\Some\beta.\psi(x,\beta) \=\mathsf{total}\\
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%% \[\exists\beta\kern-1em\:\psi(x,\beta)\\
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%% \(\:\beta\\
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%% \:\beta=\top \=(*)\\
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%% \:\psi(x,\!\top) \=\mathsf{subs}\\
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%% \:\alpha \=\elim\leftrightarrow(\ref{1})\\
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%% \*\:\alpha\\
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%% \:\psi(x,\!\top) \=\elim\leftrightarrow(\ref{1})\\
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%% \:\beta=\top \=\mathsf{func}\\
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%% \:\beta\=(*)\\
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%% \)\:\alpha=\beta \=\intro\leftrightarrow\\
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%% \:\psi(x,\alpha) \=\mathsf{subs}\\
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%% \] \:\psi(x,\alpha) \=\elim\exists\\
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%% \* \:\psi(x,\alpha)\\
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%% \(\:\alpha\\
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%% \:\alpha=\top \=(*)\\
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%% \:\phi(x,\!\top) \=\mathsf{subs}\\
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%% \*\:\psi(x,\!\top)\\
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%% \:\alpha=\top \=\mathsf{func}\\
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%% \:\alpha \=(*)\\
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%% \)\:\alpha\leftrightarrow\psi(x,\!\top) \=\intro\leftrightarrow\\
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%% \) \:\psi(x,\alpha)\leftrightarrow
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%% (\alpha\leftrightarrow\psi(x,\!\top)) \=\intro\leftrightarrow\\
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%%\end{proofbox}
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%%\end{verbatim}
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%%
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%% Syntax as follows:
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%% each line is of the form
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%% \begin{center}
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%% \meta{variables}
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%% \meta{name}
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%% \verb/\:/ \meta{formula}
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%% \verb/\=/ \meta{reason}
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%% \verb/\-/ \meta{use}
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%% \verb/\\/
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%% \end{center}
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%% where
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%% \begin{itemize}
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%% \item \meta{variables} is something like ``$x,y$'' ---
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%% it's for variables declared at the beginning of $\intro\forall$- and
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%% $\elim\exists$-boxes.
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%% \item \meta{name} is a command \verb/\label{fred}/ which
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%% defines \verb/fred/ to be the label text, which may be used anywhere
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%% as \verb/\ref{fred}/ --- see {\em The \LaTeX book.}
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%% Local labels are also available, using \macrowitharg\lbl{name}
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%% or \verb/\"/\meta{name}\verb/"/; these obey the scoping rules of
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%% the boxes.
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%% You may also refer to the previous line as \verb/\ref{-}/.
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%% \item \meta{formula} is the proposition being asserted.
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%% \item \meta{reason} is \verb/\intro\land(\ref{john},\ref{mary})/
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%% or \verb/\elim\forall(\ref{jim})/.
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%% \item \meta{use} is provided for linear logic, to record the step
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%%% which uses this one. How this accords with theory I don't yet know.
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%% \end{itemize}
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%% Note that the parts are separated by \verb/\:/, \verb/\=/ and \verb/\\/;
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%% these correspond to
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%% \begin{center}
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%% {\bf let } \meta{name} = \meta{expression} : \meta{type}
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%% \end{center}
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%% in a declarative language.
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%% The \verb/\:/, \verb/\=/ and \verb/\-/ fields are optional and may occur
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%% in any order. If any of them is repeated the last is taken.
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%% If none of them is present the \meta{variables} field is also ignored.
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%%
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%% Proof {\em boxes\/} are ``wrapped up'' as follows:
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%% \begin{itemize}
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%%% \item the whole proof in \verb/\begin{proofbox}/...\verb/\end{proofbox}/;
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%%% \item single-column boxes ($\intro\forall$, $\intro\imp$, $\elim\exists$),
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%% in \verb/\[/...\verb/\]/.
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%% \item multiple-column boxes are of two kinds:
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%% \begin{itemize}
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%%% \item separate ($\intro\land$) boxes: \verb/\(/...\verb/\*/...\verb/\)/.
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%% \item stuck together ($\elim\lor$) boxes:
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%% \verb/\(/...\verb/\+/...\verb/\)/.
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%% \end{itemize}
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%% \end{itemize}
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%% You may put more than two columns in \verb/\(/...\verb/\)/ and even mix
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%% the \verb/\+/ and \verb/\*/ separators.
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%%
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%% The whole proof is enclosed in \verb/\proofbox/...\verb/\endproofbox/
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%% or \verb/\begin{proofbox}/...\verb/\end{proofbox}/, but the \LaTeX\
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%% environment form {\em must not\/} be used for nested boxes.
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%%
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%% If the proof occurs in paragraph mode (ie in vertical or
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%% unrestricted horizontal mode) then it is set as a display, using the
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%% full width of the page. Otherwise it uses only the required width.
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%%
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%% A lot of the internals are potentially configurable, but there is not
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%% yet a user interface suitable for doing this. This will be provided
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%% in the next version.
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%%
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%% This is a {\em prototype\/} proof-box macro package;
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%% the syntax and implementation may change.
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%% It is {\tt boxproof.tex} in the \TeX\ system
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%% (so just \verb/\input boxproof/).
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%%
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%% There are some examples in
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%% \verb+~pt/utilities/proofs/proofboxeg.tex+ and
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%% \verb+proofboxeg1.tex+.
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%%
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%% The prototype version was begun on 2 August 1991, the new one on
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%% 4 June 1993.
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%%
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%%
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\message{}\edef\proofboxrestoreat
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{\noexpand\catcode`\noexpand\@\the\catcode`\@}\catcode`\@=11 \count@\year
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\multiply\count@12 \advance\count@\month\ifnum\count@> 23999 \message{}%
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\message{}\fi\let\pb@A\+\let\+\relax\let\pb@B\(\let\pb@C\)\def\pb@D{\pb@B
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\let\)\pb@C}\def\pb@E{\pb@B\displaystyle\let\]\pb@C}%%
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%% The following are user-settable dimensions.
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%%
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\newdimen\prooflinenowidth\prooflinenowidth1em \newdimen\proofboxfullwidth
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\newdimen\proofboxleftmargin\proofboxleftmargin3em \newdimen
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\proofboxrightmargin\newdimen\proofboxrulebreadth\proofboxrulebreadth.4pt
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\newdimen\proofboxseparation\proofboxseparation.2em \newdimen
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\proofboxbaselineskip\proofboxbaselineskip4ex %%
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%%
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%% The following are user-accessible numbers.
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%%
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\newcount\proofcolumns\newcount\prooflinetotal\newcount\prooflineinbox%%
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%%
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%% These boxes receive the fields of the proof steps.
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%% They are used in \verb/\proofboxmakeleftcolumn/ {\em etc}.
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%%
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\newbox\proofboxproposition\newbox\proofboxreason\newbox\proofboxuse\newbox
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\proofboxvariables%%
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%% The left-most switch is used by
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%%% \verb/\proofboxmakelabel/ to suppress the label in all but the first column.
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%% On the outside it is true.
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\newif\ifleftmostproofbox\leftmostproofboxtrue%%
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%%
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%% The following are obsolete: they are only included for reverse
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%% compatibility with the prototype version.
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\newdimen\proofboxintercol\newdimen\proofboxsurround\newdimen
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\proofboxformulawidth\newdimen\proofboxmargin\newskip\proofboxlefttabskip
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\newskip\proofboxrighttabskip%%
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%%
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%% \subsection{Redefinable macros}
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%% WARNING: most of these commands will be hidden and replaced with
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%% optional arguments to \verb/\proofbox/ in a future version.
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%% Do not rely on them.
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%%
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%% We provide three different ways of numbering the lines of the proof:
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%% \begin{itemize}
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%% \item \verb/\runningproofline/: a global running sequence (default),
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%%
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\def\runningproofline{\number\prooflinetotal}%%
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%% \item \verb/\nestedproofline/: a hierarchical system with dots,
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%%
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\def\nestedproofline{\relax\ifx\enclosingproofline\empty\else
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\enclosingproofline{.}\fi\number\prooflineinbox}\def\enclosingproofline{}%%
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%% \item \verb/\nestedproofline/: a fully hierarchical system which
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%% also includes the column number
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%% (\verb/\proof@columns/) as a letter (ASCII quote plus number).
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%%
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\def\proofboxcolumn{\ifnum\proofcolumns>\z@{\count@96\advance\count@
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\proofcolumns\char\count@}\fi}\def\fullynestedproofline{\relax\ifx
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\enclosingproofline\empty\enclosingproofline\proofboxcolumn.\else
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\proofboxcolumn\fi\number\prooflineinbox}%%
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%% \end{itemize}
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%% \verb/\theproofline/ is the default.
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%%
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\let\theproofline\runningproofline%%
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%% The macro \verb/\proofboxmakelabel#1/ is used to print the line label.
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%% We only put it in the leftmost box.
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%% It is printed in small non-ranging Arabic numerals
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%% ({\the\scriptfont1 0123456789}).
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%% Right-justify it in \verb/\prooflinenowidth/ if it will fit,
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%% otherwise let it stick out on the right, {\em i.e.}~left-justify it.
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%%
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\def\proofboxmakelabel#1{{\relax\ifleftmostproofbox\setbox\z@\hbox{\hss\the
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\scriptfont\@ne#1}\ifdim\wd\z@<\prooflinenowidth\setbox\z@\hbox to%
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\prooflinenowidth{\unhbox\z@}\fi\box\z@\quad\fi}}%%
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%% Kill the numbers altogether with \verb/\proofboxnonumbers/.
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%%
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\def\proofboxnonumbers{\def\proofboxmakelabel##1{}}%%
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%% How to make the left column of the proof box:
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%% use the variables field, a space if necessary and the line label.
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%%
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\def\proofboxmakeleftcolumn{\kern\proofboxseparation\hfil\dimen@\wd
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\proofboxvariables\unhbox\proofboxvariables\ifdim\dimen@>\z@\quad\fi
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\proofboxmakelabel\@currentlabel}%%
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%% How to make the middle column of the proof box:
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%% left justify the formula field.
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%%
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\def\proofboxmakemiddlecolumn{\unhbox\proofboxproposition\hfil\quad}%%
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%% How to make the right column of the proof box:
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%% use the reason and use fields.
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%%
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\def\proofboxmakerightcolumn{\box\proofboxreason\box\proofboxuse\hfil\kern
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\proofboxseparation}%%
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%%
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%% Make the four edges of a rectangular box and the separator
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%% between \verb/\+/ columns.
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%%
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\def\proofboxleftside{\leaders\hrule width\proofboxrulebreadth\vfill}\def
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\proofboxrightside{\leaders\hrule width\proofboxrulebreadth\vfill}\def
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\proofboxorseparator{\leaders\hrule width\proofboxrulebreadth\vfill}\def
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\proofboxtopside{\leaders\vrule height\proofboxrulebreadth depth\z@\hfill}%
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\def\proofboxbottomside{\leaders\vrule height\proofboxrulebreadth depth\z@
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\hfill}%%
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%%
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%% Use dotted lines: \verb/\dottedproofbox/.
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%%
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\def\dottedproofbox{\def\proofboxleftside{\leaders\pb@F\vfill} \def
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\proofboxrightside{\leaders\pb@F\vfill} \def\proofboxorseparator{\leaders
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\pb@F\vfill} \def\proofboxtopside{\leaders\pb@F\hfill}\def\proofboxbottomside
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{\leaders\pb@F\hfill}%%
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}\def\pb@F{\vbox to 5pt{\vss\hbox to 5pt{\hss.\hss}\vss}}%%
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%% Leave the boxes open at the bottom: \verb/\openproofbox/
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%%
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\def\openproofbox{\def\proofboxbottomside{\hfill}} %%
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%% \subsection{Miscellaneous logical notations}
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%%
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%% Print the names of the introduction and elimination rules, for example:
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%% \begin{quote}
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%% \verb/\elim\forall/ $\elim\forall$ \qquad
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%% \verb/\intro\land/ $\intro\land$ \qquad
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%% \end{quote}
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\def\intro#1{{{#1}{\cal I}}}\def\elim#1{{{#1}{\cal E}}}%%
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%% Recall that in \TeX\ the logical connectives and quantifiers are called
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%% \begin{center}
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%% \verb/\lor/ $\lor$\quad
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%% \verb/\land/ $\land$\quad
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%% \verb/\lnot/ $\lnot$\quad
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%% \verb/\forall/ $\forall$\quad
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%% \verb/\exists/ $\exists$
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%% \end{center}
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%% The following provide macros for the \verb/\implies/ {\em relation\/}
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%% and for the binary {\em operation\/} which yields the abstract
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%% \verb/\implic/ation between formulae.
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%% The point is that \TeX\ spaces them and breaks the lines differently:
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%% \begin{center}
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%% \verb/A\implies B/ $A\implies B$\quad{\em versus\/}\quad
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%% \verb/A\implic B/ $A\implic B$
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%% \end{center}
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%% There are forward and reverse, single and Double versions.
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%%
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\mathchardef\implies="3221 \mathchardef\impliedby="3220 \mathchardef\Implies=%
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"3229 \mathchardef\Impliedby="3228 \mathchardef\implic="2221 \mathchardef
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\implicby="2220 \mathchardef\Implic="2229 \mathchardef\Implicby="2228 \let
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\imp\to%%
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%% Handle the spacing after a variable (and optionally its type)
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%% bound by a quantifier symbol. For example
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%% \begin{quote}
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%% \verb/\All x:X. \phi(x)/\quad prints as\quad $\All x:X.\phi(x)$\quad
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%% instead of\quad $\forall x:X.\phi(x)$
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%% \end{quote}
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\def\Quantifier#1#2.{\pb@G{#1}#2::.}\def\pb@G#1#2:#3:#4.{{{#1}{#2}\def\next{#%
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3}\ifx\next\empty{.}\mkern4mu \else\mkern1mu{\colon}\mkern1mu{#3}\mkern.5mu{.%
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}\mkern6mu \fi}}%
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%% We provide some commonly used forms; \verb/\iota/ ($\iota$) is Russell's
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%% description operator and should really be inverted.
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\def\All{\Quantifier\forall}\def\Some{\Quantifier\exists}\def\Function{%
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\Quantifier\lambda}\def\Product{\Quantifier\Pi}\def\Sum{\Quantifier\Sigma}%
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\def\TheOne{\Quantifier\iota}\def\Least{\Quantifier\mu}\def\Greatest{%
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\Quantifier\nu}%%
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%% There are several notations for substitution.
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%% After writing $a[x:=b]$ throughout my book I~thought I~might change to
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%% $[b/x]^*a$.
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%% This macro reads the source in the first form and prints in the second.
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%% If you use it you can, like me, defer the decision about
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%% which notation to use until the final stages, doing
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%% \begin{quote}
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%% \verb/\renewcommand{\Subst}{\plainsubstitution}/
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%% \end{quote}
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%% if you finally decide on making substitution act on the right.
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%% This is already an improvement on the literal text, because it
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%% automatically enlarges the brackets according to the text inside.
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%% \verb/\Subst/ itself is (following my book)
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%% defined in terms of the action of a context morphism (\verb/\CtxtMor/)
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%% on a term. Again you can do
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%% \begin{quote}
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%% \verb/\renewcommand{\CtxtMor}{\plaincontextmorphism}/
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%% \end{quote}
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%% for something simpler.
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%% This macro interprets its argument as a comma-separated list
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%% of items in the form $x:=b$, which it switches to $b/x$.
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\def\swappingsubstitution#1[#2]{{\CtxtMor[#2]^*{#1}}}%
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%\def\swappingcontextmorphism[#1]{{\let\pb@J\empty\left[\pb@H#1,[],\/\right]}}%
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\def\swappingcontextmorphism[#1]{{\let\pb@J\empty[\pb@H#1,[],\/]}}%
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\def\pb@H#1,{\def\next{#1}\ifx\next\pb@K\else\pb@J\let\pb@J,\pb@I#1:=:=,%
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\expandafter\pb@H\fi}\def\pb@I#1:=#2:=#3,{{\def\next{#2}\ifx\next\empty\else{%
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#2}/\fi{#1} }}\def\pb@K{[]}\def\Subst{\swappingsubstitution}\def\CtxtMor{%
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\swappingcontextmorphism}%%
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%% The simple versions.
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\def\plainsubstitution#1#2{{#1}{\left[{#2}\right]}}\def\plaincontextmorphism#%
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1{{\left[#1\right]}}\newbox\pb@L\newdimen\pb@T\newdimen\pb@U\newdimen\pb@M
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\newdimen\pb@N\newdimen\pb@O\newdimen\pb@P\newdimen\pb@Q\newdimen\pb@R
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\newdimen\pb@S\def\pb@V#1#2{\relax\ifdim#1<#2\relax#1=#2\relax\fi}\count@
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\year\multiply\count@12 \advance\count@\month\ifnum\count@> 25000 \message{%
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because this one has expired and will no longer work!}\endinput\fi%%
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\def\proofbox{\relax\ifmmode\let\next\pb@a\else\let\next\pb@b\ifhmode\ifinner
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\let\next\pb@a\fi\fi\fi\next\global\prooflinetotal\@ne\boxmaxdepth\maxdimen
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\def\[{\pb@w\pb@f\pb@W}\def\({\pb@w\pb@f\pb@X}\def\proofbox{\[}\let\lbl\pb@y
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\def\"##1"{\pb@y{##1}}\def\:{\pb@v\proofboxproposition\displaystyle}\def\={%
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\pb@v\proofboxreason}\def\-{\pb@v\proofboxuse}\def\\{\pb@w\pb@u}\let\+\pb@c
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\let\*\pb@c\let\]\pb@c\pb@p\pb@s}\def\endproofbox{\pb@q\pb@IA\box\pb@L\egroup
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}\def\pb@W{\let\+\pb@d\let\*\pb@d\def\){\pb@e\[\)}\let\]\pb@Y\proofcolumns\z@
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}\def\pb@X{\proofcolumns\@ne\def\+{\pb@j\pb@l}\def\*{\pb@j\pb@m}\def\]{\pb@e
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\(\]}\let\)\pb@Y}\def\pb@Y{\pb@o\pb@u}\def\pb@a{\hbox\bgroup}\def\pb@b{$$%
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\kern-\displayindent\hbox to\hsize\bgroup\proofboxfullwidth\hsize\aftergroup$%
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\aftergroup$}\def\pb@c{\errmessage{Box proofs: \string\+, \string\*, \string
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\) and \string\] may not be used at the top level}}\def\pb@d{\errmessage{Box
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proofs: enclose \string\+ and \string\* in \string\(\string\), not \string\[%
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\string\]}}\def\pb@e#1#2{\errmessage{Box proofs: \string#1 closed by \string#%
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2}\pb@Y}\def\pb@f#1{\setbox\pb@L\hbox\bgroup#1\let\pb@g\pb@n\let
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\enclosingproofline\@currentlabel\edef\pb@h{\the\prooflinetotal}\let\pb@i
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\pb@h\pb@O\z@\pb@M\z@\pb@N-\maxdimen\pb@P\z@\pb@p\pb@t}\def\pb@j#1{\pb@q\pb@k
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\let\pb@g#1\advance\proofcolumns\@ne\global\prooflinetotal\pb@h
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\leftmostproofboxfalse\pb@p\pb@t}\def\pb@k{\pb@g\pb@V\pb@M{\wd\pb@L}\advance
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\pb@O\wd\pb@L\ifnum\pb@i<\prooflinetotal\edef\pb@i{\the\prooflinetotal}\fi
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\ifdim\pb@N<\dp\pb@L\pb@N\dp\pb@L\pb@P\pb@Q\fi\setbox\z@\hbox{%
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\proofboxtopside}\wd\z@\z@\box\z@\setbox\z@\hbox{\proofboxbottomside}\wd\z@
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\z@\box\z@\kern\pb@R\box\pb@L\kern\pb@S}\def\pb@l{\vtop{\proofboxorseparator}%
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\penalty\thr@@}\def\pb@m{\vtop{\proofboxrightside}\kern\proofboxseparation
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\vtop{\proofboxleftside}\penalty\tw@}\def\pb@n{\pb@T\pb@R\setbox\z@\vtop{%
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\proofboxleftside}\dimen@\wd\z@\advance\pb@T\dimen@\advance\pb@T
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\proofboxseparation\kern-\pb@T\kern\proofboxseparation\box\z@\penalty\@ne}%
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\def\pb@o{\pb@q\pb@k\setbox\z@\vtop{\proofboxrightside}\global\advance\pb@S
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\wd\z@\box\z@\global\advance\pb@S\proofboxseparation\kern\proofboxseparation
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|
\global\prooflinetotal\pb@i\global\pb@R\pb@T\global\pb@Q\pb@P\ifnum
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\proofcolumns<\@ne\proofcolumns\@ne\fi\penalty\proofcolumns\kern-\pb@M\kern
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\pb@M\kern-\pb@O\kern\pb@O\kern-\pb@S\penalty\@ne\egroup\pb@r}\def\pb@p#1{%
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\setbox\pb@L\vtop\bgroup\baselineskip\proofboxbaselineskip\prooflineinbox\@ne
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\pb@T\z@\pb@U\z@#1\pb@u}\def\pb@q{\pb@w\global\pb@R\pb@T\global\pb@S\pb@U
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\egroup}\def\pb@r{\pb@V\pb@T\pb@R\pb@V\pb@U\pb@S\box\pb@L\prevdepth\pb@Q}\def
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\pb@s{}\def\pb@t{}\def\pb@u{\edef\@currentlabel{\theproofline}\let\label@name
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\@currentlabel\setbox\proofboxproposition\box\voidb@x\setbox\proofboxreason
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|
\box\voidb@x\setbox\proofboxuse\box\voidb@x\setbox\proofboxvariables\hbox
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|
\bgroup\let\pb@z\pb@AA\let\pb@w\pb@x$}\def\pb@v#1{$\egroup\setbox#1\hbox
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|
\bgroup\let\pb@z\pb@AA$}\def\pb@w{$\egroup\global\advance\prooflinetotal\@ne
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|
\advance\prooflineinbox\@ne\setbox\pb@L\hbox{\setbox\z@\hbox{%
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|
\proofboxmakeleftcolumn}\global\pb@R\wd\z@\kern-\pb@R\box\z@\hbox{%
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|
\proofboxmakemiddlecolumn}\setbox\z@\hbox{\proofboxmakerightcolumn}\global
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|
\pb@S\wd\z@\box\z@\kern-\pb@S\penalty\tw@}\global\pb@Q\dp\pb@L\pb@r}\def\pb@x
|
|
{$\egroup}\def\pb@y#1{\aftergroup\pb@z\expandafter\aftergroup\csname r@#1%
|
|
\endcsname}\def\pb@z#1{\edef#1{{\@currentlabel}{}}\expandafter\pb@@A\string#1%
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|
\\}\expandafter\def\expandafter\pb@@A\string\r@#1\\{\def\label@name{#1}}\def
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|
\pb@AA#1{\aftergroup\pb@z\aftergroup#1}\expandafter\def\csname r@-\endcsname{%
|
|
{\previous@label}{}}\dimendef\pb@BA=\@ne\dimendef\pb@CA=\tw@\dimendef\pb@DA=%
|
|
\thr@@\dimendef\pb@EA=4 \dimendef\pb@FA=5 \dimendef\pb@GA=6 \chardef\pb@HA=9
|
|
\def\pb@IA{\pb@GA\proofboxfullwidth\pb@T\proofboxleftmargin\pb@V\pb@T\pb@R
|
|
\advance\pb@GA-\pb@T\pb@U\proofboxrightmargin\pb@V\pb@U\pb@S\advance\pb@GA-%
|
|
\pb@U\pb@V\pb@GA{\wd\pb@L}\pb@JA}\def\pb@JA{\setbox\pb@L\vtop{\unvbox\pb@L
|
|
\loop\skip@\lastskip\unskip\setbox\pb@HA\lastbox\ifhbox\pb@HA\pb@KA\repeat
|
|
\unvbox\pb@L\unskip}}\def\pb@KA{\pb@DA\dp\pb@HA\pb@EA\ht\pb@HA\pb@CA\wd\pb@HA
|
|
\setbox\pb@HA\hbox{\unhbox\pb@HA\count@\lastpenalty\unpenalty\unkern\ifodd
|
|
\count@\pb@LA\else\setbox\thr@@\lastbox\setbox\tw@\lastbox\setbox\@ne\lastbox
|
|
\unkern\hbox to\pb@T{\unhbox\@ne}\hbox to\pb@GA{\unhbox\tw@}\hbox to\pb@U{%
|
|
\unhbox\thr@@}\fi}\dp\pb@HA\pb@DA\ht\pb@HA\pb@EA\setbox\pb@L\vtop{\box\pb@HA
|
|
\nointerlineskip\vskip\skip@\unvbox\pb@L}}\def\pb@LA{\pb@O\lastkern\unkern
|
|
\unkern\pb@M\lastkern\unkern\unkern\proofcolumns\lastpenalty\unpenalty\pb@FA
|
|
\pb@T\ifnum\@ne=\proofcolumns\let\pb@MA\pb@NA\else\advance\pb@GA-\pb@CA\pb@BA
|
|
\pb@GA\advance\pb@GA\pb@O\ifdim\pb@GA<\proofcolumns\pb@M\divide\pb@BA
|
|
\proofcolumns\let\pb@MA\pb@PA\else\divide\pb@GA\proofcolumns\let\pb@MA\pb@OA
|
|
\fi\fi\dimen@\lastkern\unkern\setbox\@ne\lastbox\pb@RA\setbox\pb@HA\hbox{\box
|
|
\@ne\kern\dimen@}\advance\pb@U-\wd\pb@HA\unkern\loop\setbox\pb@L\lastbox\pb@T
|
|
\lastkern\unkern\setbox\tw@\lastbox\setbox\thr@@\lastbox\count@\lastpenalty
|
|
\unpenalty\pb@MA\pb@JA\setbox\@ne\vbox{\offinterlineskip\pb@QA\thr@@\vfil
|
|
\pb@QA\tw@}\pb@RA\pb@TA{\box\@ne\box\pb@L}\ifnum\count@>\@ne\pb@SA\pb@U
|
|
\lastkern\unkern\repeat\unhbox\pb@HA}\def\pb@NA{\pb@T\pb@FA\setbox\@ne
|
|
\lastbox\advance\pb@T-\wd\@ne\dimen@\lastkern\unkern\unkern\kern\dimen@\pb@RA
|
|
\box\@ne\advance\pb@T-\dimen@}\def\pb@OA{\ifnum\@ne=\count@\pb@NA\fi}\def
|
|
\pb@PA{\pb@GA\wd\pb@L\advance\pb@GA\pb@BA\pb@OA}\def\pb@QA#1{\setbox#1\hbox to%
|
|
\wd\pb@L{\unhbox#1}\wd#1\z@\box#1\relax}\def\pb@RA{\setbox\@ne\vbox to\pb@EA{%
|
|
\offinterlineskip\vskip-\proofboxseparation\unvbox\@ne\vskip-%
|
|
\proofboxseparation\setbox\z@\null\ht\z@-\pb@DA\dp\z@\pb@DA\box\z@}}\def
|
|
\pb@SA{\setbox\@ne\lastbox\pb@RA\pb@TA{\box\@ne}\ifodd\count@\else\dimen@
|
|
\lastkern\unkern\setbox\@ne\lastbox\pb@RA\pb@TA{\box\@ne\kern\dimen@}\fi}\def
|
|
\pb@TA#1{\setbox\pb@HA\hbox{#1\unhbox\pb@HA}}\let\+\pb@A\proofboxrestoreat
|
|
\endinput\def\x{}%%
|
|
%% \end{document}
|
|
% \fi
|