\message{}
%%========================================================================
%************************************************************************%
%* *%
%* Maybe you already have a \qed macro to put a little square *%
%* on the right hand side at the end of a mathematical proof? *%
%* *%
%* IT'S PROBABLY MINE! *%
%* *%
%* Please compare yours with \parag@pushright below. *%
%* *%
%* This new file is compatible, it fixes the bugs, has extra *%
%* features, and is maintained and portable. Please use it! *%
%* *%
%* NEW FEATURE \WillHandleQED and \HandleQED for environments *%
%* which do not give access to the right hand side of the page. *%
%* *%
%* Now also available: \DefineStandardTheorems or *%
%* \usepackage[define-standard-theorems]{QED} *%
%* *%
%************************************************************************%
%========================================================================%
% COPYRIGHT (C) 1993-6 Paul Taylor, Department of Computer Science,
% Queen Mary & Westfield College, London E1 4NS.
% You may use this file for any purpose. You may copy it on condition that
% you do so in exactly the form in which it was supplied, make no charge
% for the copy and impose the same conditions on the recipient.
% This software is supplied ``as is'' without warranty, express or implied,
% including but not limited to merchantability and fitness for any particular
% purpose. No liability is accepted by the author, Queen Mary and Westfield
% College, Imperial College or any third party for any direct or consequential
% damages, however caused.
% In all cases you must keep several backup versions of your files in a place
% to which your machine cannot write, and you must check documents visually
% before submitting the final version to a publisher or expensive printer.
% WARNING: If you use this with Frank Mittlebach's "theorem.sty" you
% MUST load theorem first, then QED, then do the \newtheorem commands.
% Authoritative version: /pub/tex/contrib/pt/proofs/QED.sty
% by anonymous FTP from: ftp.dcs.qmw.ac.uk
% also CTAN: macros/generic/proofs/taylor/QED.sty
% author/maintained by: Dr Paul Taylor
% WARNING: This file replaces some of the functions of "Paul.sty"
% and MUST NOT be used with it as serious conflicts will arise.
%=========================================================================
% USER INTERFACE AND EXAMPLES (see also OPTIONS below)
% LaTeX2e \usepackage options: see \DeclareOption commands below
% theorems-as-commands roman-theorems italic-theorems
% auto-QED explicit-QED number-theorems dont-number-theorems
% black-square open-square
% \begin{Proof} ... \end{Proof}
% or \Proof ... \endProof
% or \Proof ... \endproof
% or \Proof ... \qed also \QED \QEF and \QEI
% WARNING: \qed which doesn't follow \Proof will not print the square.
% Each properly nested Proof/endProof pair gets a single
% \qedsymbol at the end, on the far right hand side.
% Unfortunately, this may still be in the wrong place
% if the proof ends with a display or itemisation.
% To solve this, \qed may be put *inside* the last substantive
% environment; the \qedsymbol will be put at that point
% (the visual end) and suppressed at the logical end of proof.
% Examples:
% \begin{Proof} \begin{Proof}
% ... ...
% \begin{eqnarray} \begin{itemize}
% ... &=& ... \\ \item ...
% .. &=& ... &\qed \item ... \qed
% \end{eqnarray} \end{itemize}
% \end{Proof} \end{Proof}
% also works with $$...$$ and \[...\] displays, including fleqn.sty.
% Unfortunately some environments, such as picture, do not allow this at all.
% See the section "centering environments" below for the mechanism for
% passing \qed to such an environment for special processing.
% In fact \qed will only work in those environments which provide access to
% the right hand side of the page. In other words, wherever you think
% "\hfill\square" ought to work then \qed will; of course it is just because
% that naive method doesn't work that this macro file is needed at all.
% The macro was designed to solve the problem in the case of "unrestricted
% horizontal mode" (ie at the end of a paragraph); it also works in $$
% displays by pretending to be an equation number. In most other cases it
% basically does "\hfill\square" or "\hfill$\square$" and hopes for the best.
% If you have to put \qed outside the environment, it may be appropriate to
% put \vskip-\baselineskip before it, unless of course this would over-print.
% There is, however, still a danger that TeX will break the page here.
% This seems to be unavoidable if the environment ends with a \penalty.
% The eqnarray example above does not in fact work: if you try it you'll
% get "! Paragraph ended before \llap was complete" with LaTeX in a mess.
% This is a very common place where you might want to put the end of proof
% mark, and I also consider that the fourth column should be available for
% "reasons" for equational steps. The following substitute for \eqnarray
% allows this, whilst being compatible with automatic numbering. I have
% proposed it to Rainer Sch\"opf for inclusion in LaTeX. If you want to
% use it, please copy it to another file rather than uncommenting it here.
% Don't forget to use \makeatletter or put it in a documentstyle (.sty) file.
%
% \def\eqnarray{\stepcounter{equation}\let\@currentlabel\theequation
% \global\@eqnswtrue\m@th\global\@eqcnt\z@\tabskip\@centering\let\\\@eqncr
% $$\halign to\displaywidth\bgroup\@eqnsel\hskip\@centering$\displaystyle
% \tabskip\z@{##}$&\global\@eqcnt\@ne\hskip 2\arraycolsep \hfil${##}$\hfil
% &\global\@eqcnt\tw@\hskip2\arraycolsep$\displaystyle\tabskip\z@{##}$\hfil
% \tabskip\@centering&%
% \global\@eqcnt\thr@@\hbox to\z@\bgroup\hss##%*** instead of "\llap{##}"
% \tabskip\z@\cr}%
% \def\@@eqncr{\let\@tempa\relax
% \ifcase\@eqcnt \def\@tempa{& & &}\or \def\@tempa{& &}%
% \or\def\@tempa{&}\else\@eqnswfalse%*** instead of "\else\def\@tempa{&}"
% \fi\@tempa\if@eqnsw\@eqnnum\stepcounter{equation}\fi
% \egroup%*** added, to match \bgroup in fourth cell of preamble
% \global\@eqnswtrue\global\@eqcnt\z@\cr}
% Why can't we do all of this with \endProof? Because by that stage
% the damage has been done: the environments, paragraphs or
% displays have already been closed and their \hbox'es added
% to the current vertical list, and cannot be removed for
% alteration if this is the current page.
% Even if you don't need to put \qed inside an inner environment
% to avoid a blank line, it's still a good idea to do so, because
% otherwise it's possible that intervening end-of-environment
% material may allow TeX to put the mark on the next page.
% This file may be called QED.sty, QED.tex, qed.sty or qed.tex.
% It may be loaded using \input, \usepackage or as a \documentstyle option,
% as it is careful to handle the \catcode of @ appropriately.
% If you don't use theorem.sty, this file instead provides options to use
% commands to begin theorems, instead of enclosing them in environments,
% and to suppress numbering and italicisation. A rudimentary version of
% \newtheorem for plain TeX is also implemented (always using commands
% rather than environments).
% At the end of the file some useful \newtheorem
% commands are listed but not executed.
% NB \Theorem\Proof\endProof\qed will print the second square, whereas
% \begin{Theorem}\end{Theorem}\begin{Proof}\end{Proof}\qed will not.
%=========================================================================
% Make @ letter, saving its old code to restore at the end of this file.
% Look for this towards the end of the file if you think something's missing!
% "plain.tex" defines \lq as a synonym for back quote (character constant);
% I use it to avoid corruption when sending TeX files by email via BITNET.
\edef\qedrestoreat{\noexpand\catcode\lq\noexpand\@=\the\catcode\lq\@}%%
\catcode\lq\@=11
% in LaTeX, \protect the user commands;
% in plain TeX, ensure that it is defined.
\ifx\protect\undefined\let\protect\relax\fi
%=========================================================================
% OPTIONS
% These are the user commands.
\def\qed{\protect\@qed{$\qedsymbol$}}% suppressible printing of \qedsymbol
% \pushright takes an argument, which it always prints
% it is (re)defined by \WillHandleQED and \UnHandleQED below (12.4.94)
% theoremata in Euclid needed proof: "which was to be shown"
\def\QED{\protect\@qed{{\rm Q.E.D.}}}% "quod erat demonstrandum"
% but problemata needed construction: "which was to be found"
\def\QEI{\protect\@qed{{\rm Q.E.I.}}}% "quod erat inveniendum"
% alternatively: "which was to be done/made"
\def\QEF{\protect\@qed{{\rm Q.E.F.}}}% "quod erat faciendum"
% a LaTeX environment
\def\Proof{\protect\@Proof}\def\endProof{\protect\@endProof}%
\let\proof\Proof\let\endproof\endProof
% These are the user-settable parameters.
% The actual (maths) symbol used by \qed
\def\qedsymbol{\square}% PLEASE NOTE: this is in the AMS symbols font.
%\def\qedsymbol{\blacksquare}% use one of these instead
%\def\qedsymbol{\hbox{\rm Q.E.D.}}% if you prefer
%\def\qedsymbol{\dashv}% this is what the Journal of Symbolc Logic likes.
% This is the text used by \Proof.
% A new paragraph is begun without indentation.
% Change it to {\kern\parindent\sc D\'emonstration: } if you like.
\def\TheWordProof{\bf Proof\enskip}
% This is the font command used for the text of proofs
\def\ProofFont{}
% The command \AutoQEDtrue causes a \qed in \end{Theorem}, so you do
% \begin{Theorem} ... \begin{Proof} ... \end{Proof} \end{Theorem}
% but if you omit the proof, the statement gets a little square at the end.
\newif\ifAutoQED\AutoQEDfalse
% The remaining options are redundant with theorem.sty
% so are not defined if this has been loaded.
\newif\ifNumberResults
\ifx\theorem@style\undefined
%
% How to print the name (#1), number (#2) and attribution (#3) of a theorem.
\NumberResultstrue
% If the number (#2) is absent, "\unskip" removes the
% unwanted space "\ " from before it (16 Feb 1993).
\def\TheoremHeader#1#2#3{\bf #1\ifNumberResults\ #2\unskip\fi#3}
%
% This is the font command used for the text of theorem enunciations
% change to {\rm} or {\small} if you like.
\def\TheoremFont{\it}
%
% The command \NumberResultsfalse will suppress theorem numbering.
%
% The command \TheoremsAsCommands will allow you to write
% \Theorem instead of \begin{Theorem} ... \end{Theorem}.
% In this case italicisation is suppressed by default.
% To do this with theorem.sty would involve rewriting the substyles.
%
% WARNING: if you subsequently redefine \TheoremFont, and use the command
% instead of the environment, the font will remain in force afterwards!
\fi
% The document style option "theorems-as-commands" will allow you to
% write \Theorem instead of \begin{Theorem} ... \end{Theorem}.
% Moved here from further down. 10 Jan 1994
\def\TheoremsAsCommands{%
\def\TheoremFont{}% suppress italicised theorems.
\def\begin@theorem##1{%
\par\removelastskip\smallskip
\save@set@qed % enable \qed
\noindent{##1}% the name
%\TheoremFont % italicise at your own risk!
}%
\def\@endtheorem{\ifAutoQED\qed\fi\restore@qed}%
}%
\expandafter\let\csname ds@theorems-as-commands\endcsname\TheoremsAsCommands
%=========================================================================
% If you already have a macro called \qed, \endproof or \pushright
% which is laid out in a similar way to the following two definitions
% (but with \hbox@pushright incorporated) then it is almost certainly
% my code, which has been copied anonymously via numerous people since
% my Cambridge PhD thesis in August 1986. Belated acknowledgements to
% Chris Thompson of the Cambridge University Computing Service for his
% help with my early attempts at TeX, in particular this problem.
% The complexity of the macro necessary to get a little box on the
% right-hand-side at the end of a proof is amazing. It really does
% have to be this long! Otherwise you're liable to get it at the
% beginning of the next line, or even on the next page.
\def\parag@pushright#1{{% set up
\parfillskip=0pt % so \par doesnt push \square to left
\widowpenalty=10000 % so we dont break the page before \square
\displaywidowpenalty=10000 % ditto
\finalhyphendemerits=0 % TeXbook exercise 14.32
%
% horizontal
%\leavevmode % not needed since we now only use it in hmode
\hbox@pushright % this used to be incorporated
#1% % the end-of-proof mark (or whatever)
%
% vertical
\par}}% % build paragraph with the above parameters
\def\hbox@pushright{% horizontal
\unskip % remove previous space or glue
\nobreak % don't break lines
\hfil % ragged right if we spill over
\penalty50 % discouragement to do so
\hskip.2em % ensure some space
\null % anchor the following \hfill
\hfill % push \square to right
}%
% Ideally \endProof should do all this. We should be able to add the symbol
% to the last line after the paragraph, display or whatever other structure
% has been completed and we've returned to vertical mode. This isn't possible
% on the current page (outer vmode) because \lastbox doesn't work there.
% But \ifinner is true inside a \vbox, \vadjust or \insert (LaTeX \parbox,
% minipage, figure or table), and in these circumstances we can use \lastbox.
% We would have to strip & restore glue & penalties (\insert, \mark and \write
% are obstacles to this) to get access to the last line (box), which may
% still not have the correct baseline. We could check its natural width
% against the page width, but if we re-set it, centering and (right)
% justification might be disturbed. Is this worth the trouble?
\def\vbox@pushright#1{\expandafter\message % (2 Jan 1994)
{QED.sty could be improved in this case (line \the\inputlineno): please ask}%
\page@pushright{#1}}%
% Using this method the Proof environment could be implemented by collecting
% the entire proof in its own \vbox, modifying that and \unvbox'ing it to the
% current page. This approach may lead to the following problems:
% (i) footnotes, floats, marginpars, labels and index items may be lost;
% (ii) overflow of TeX's main memory, especially if \end{Proof} is missing;
% (iii) I don't know how page-breaking would be handled.
%========================================================================
% Switch to enable/suppress \qedsymbol; since suppression may be done
% within a nested scope it must be global, so we do our own save/restore
% in a symbol which is local to the Proof environment.
% On first use, we check to see whether an obsolete version of Paul.sty
% is around, and complain loudly if it is, because they interfere seriously.
\newif\if@qed\@qedfalse
\def\save@set@qed{\check@pt@sty@v\let\saved@ifqed\if@qed\global\@qedtrue}%
\def\restore@qed{\global\let\if@qed\saved@ifqed}
% prefer proofs with statements if possible - hence \penalty700
% the only essential part of this is \save@set@qed
\def\@Proof{%
\par\removelastskip\smallskip\penalty700
\save@set@qed
\noindent\ProofFont{\TheWordProof\enskip}%
}%
\def\@endProof{%
\qed\restore@qed
\penalty-700 \smallskip
}
\def\@qed#1{\check@pt@fm@thm
\if@qed % have we already done \qed?
\global\@qedfalse\pushright{#1}% - no - do it now, but not again
\else\ifhmode\ifinner\else\par\fi\fi% - yes - just end paragraph, if any
\fi}
% \pushright{text} always prints its argument, on the far right, in text mode
\def\@pushright#1{%
\ifvmode
\ifinner\vbox@pushright{#1}% vertical mode (see comments above)
\else \page@pushright{#1}%
\fi
\else\ifmmode\maths@pushright{\hbox{#1}}% maths (force a text argument)
\else\ifinner\hbox@pushright{#1}% inside an \hbox
\else\parag@pushright{#1}% in a paragraph
\fi \fi \fi
}% (22 Feb 1993) removed extra {} which would destroy our \] below
% In the \hbox and maths cases we are really at the mercy of the environment.
% Assuming that we have $\qed$ simply embedded in a paragraph, the horizontal
% processing by \hbox@pushright will at least make sure that the square isn't
% at the beginning of the line, but we can't stop it being on the next page.
% However it is more likely that the reason why we're in maths mode is that
% we're inside an eqnarray or similar, in which case \hfill will do its best
% to put the square on the right of the available space. (See \vadjust below.)
\def\maths@pushright#1{%
\ifinner
\hbox@pushright{#1}%
\else
\eqno#1% use TeX's right equation number feature (\eqno) within $$.
\def\]{$$\ignorespaces}% suppress LaTeX's error checking (HACK!)
\fi
}% (22 Feb 1993) removed extra {} which would destroy our \] above
% outer vertical mode (the current page)
% There's very little we can do in these circumstances!
% Penalties still allow the page to be broken.
% If the user has put negative glue in, leave it alone. (15 Feb 1994)
\def\page@pushright#1{% 18 Jan 1994
%\unpenalty % ineffective
\skip@\lastskip
\ifdim\skip@>\z@
\unskip % remove \parskip, but only (15 Feb 1994) if it's positive
\else\skip@\z@\relax
\fi
%\unpenalty % TeX won't let me do this
\dimen@\baselineskip
\advance\dimen@-\prevdepth % save \prevdepth to make a strut
\nobreak % don't break the page here
\nointerlineskip
\hbox to\hsize{%
\setbox\z@\null
\ifdim\dimen@>\z@\ht\z@\dimen@\fi % simulate \baselineskip
\box\z@
\hfill
#1}%
\vskip\skip@ % replace old \parskip
}%
% An idea that didn't work: see TeXbook p188. (16 Feb 1993)
% Use \predisplaysize to find out the width of the previous box,
% in the case where it has already been completed.
% But this can only be used inside displays ($$), and a display in
% vertical mode begins a paragraph first, so we end up with
% \predisplaysize=\parindent+2em whatever happened in the previous
% paragraph.
% Another idea: it may be worth trying \vadjust, if only to insert \nobreak.
% The problem with this is that if we are too deeply nested in horizontal
% or maths lists, the adjustment may not be able to find its way out to the
% enclosing vertical list. In the case of array-like environments, it will
% appear (assuming it manages to get out) after the current row of the array.
%===========================================================================
% We have to add to the theorem environments the commands to enable \qed.
% This is done by re-defining \@thm#1#2.
% Note that Mittelbach's theorem.sty re-defines \@thm and \@endtheorem, so
% that must be loaded before us, otherwise our changes will get over-written
% and \qed will never be enabled.
% Paul.sty didn't use this method of gaining control inside a theorem,
% whereas it did define \qed and \pushright, so here is the one place
% where we can check for it.
\ifx\nonqed@thm\undefined % otherwise double loading causes a loop 22 Feb 1993
\let\nonqed@thm\@thm % save original
\let\nonqed@endthm\@endtheorem
\fi
\def\@thm{\save@set@qed\nonqed@thm}%
\def\@endtheorem{\ifAutoQED\qed\fi\restore@qed\nonqed@endthm}%
%===========================================================================
% "CENTERING" ENVIRONMENTS -
% those which don't give their contents access to the right hand side
% of the page, such as center, picture, ... (12 April 1994)
% Each individual environment (both the standard ones and those defined
% by the user) needs to co-operate in order to make \qed and \pushright work.
% It is not the business of this package to rewrite LaTeX in this way,
% but the following mechanism may be inserted in to other environments.
% - put \WillHandleQED in the \begin part of the environment definition;
% then if a \qed occurs in the body of the environment it is stored
% in \QEDbox until...
% - \HandleQED anywhere in the \end part of the environment definition
% (even inside dollars, braces or another environment) prints it.
%
% For example:
% \newenvironment{qedpicture}%
% {\begin{picture}\WillHandleQED}%
% {\put(0,0){\HandleQED}\end{picture}}
%
% To make this compatible with *not* loading QED.sty,
% add the following to macro files which use \WillHandleQED and \HandleQED:
% \ifx\WillHandleQED\undefined
% \let\WillHandleQED\relax
% \let\HandleQED\relax
% \let\UnHandleQED\relax % if you use it
% \let\QEDbox\voidb@x % must have \makeatletter here!
% \fi
%
% \UnHandleQED restores normal processing; this may be useful for
% the minipage environment, which has its own notion of "right hand side"
% of the page.
%
% The width of the saved \qed is available for testing as \wd\QEDbox
\newbox\qed@box % the box in which to save \qed for special handling
\def\WillHandleQED{\relax
\ifx\HandleQED\nohandle@qed
% no enclosing environment has declared \WillHandleQED
\def\pushright{\global\setbox\qed@box\hbox}% \qed will be saved
\let\QEDbox\qed@box % point at the right box
\def\HandleQED{\unhbox\QEDbox}% print it
\aftergroup\check@handle@qed % check that this really gets done
\else
% an enclosing environment already wants to catch \qed
% \HandleQED doesn't print anything - let the saved \qed pass through
\let\QEDbox\voidb@x % by pointing at an empty box
\fi}
\def\nohandle@qed{%
\errhelp{One of them is missing: see QED.sty.}%
\errmessage{This environment uses \string\WillHandleQED\space and
\string\HandleQED\space incorrectly}}
\def\check@handle@qed{\relax
\ifvoid\qed@box\else\expandafter\nohandle@qed\fi}
\def\UnHandleQED{%
\let\HandleQED\nohandle@qed
\let\QEDbox\voidb@x
\def\pushright{\protect\@pushright}}%
\UnHandleQED
%===========================================================================
% Check for obsolete versions and clashes of this and other macro files.
% Why do I do this? Because of those people who complain to me that
% something doesn't work but refuse to read the manual, and those
% who refuse to update their software, and then publish papers with
% commutative diagrams full of the bugs which I fixed several years ago.
\def\obsolete@pt@version#1{\errhelp={%
% *****************************************************************
% * The master version is available by *
Anonymous FTP ftp.dcs.qmw.ac.uk /pub/tex/contrib/pt/tex/#1}%*
% *****************************************************************
\errmessage{You have an obsolete version of #1 - please get a new one}}%
% First check QED.sty
%\ifnum\year>1996 \obsolete@pt@version{QED.sty}\fi
% If theorem.sty hasn't been loaded, arrange to check it again in \@qed.
% And check (then) whether you've actually defined \square.
% changed 2 June 1993: don't define it now, as that would confuse amssymb.sty
\ifx\theorem@style\undefined
\def\check@pt@fm@thm{\relax
\ifx\square\undefined
\gdef\square{\bigcirc
\errhelp={Anonymous ftp e-math.ams.com /ams/amsfonts}%
\errmessage{\string\square\space is an AMS symbol}%
\global\let\square\bigcirc}%
\fi
\ifx\theorem@style\undefined
\global\let\check@pt@fm@thm\relax
\else\errhelp={The macros \@thm and \@endtheorem need to be re-defined.}%
\errmessage{QED.sty must be loaded AFTER theorem.sty but before
using \string\newtheorem}%
\fi
\global\let\check@pt@fm@thm\relax
}%
\else
\def\check@pt@fm@thm{%
\ifx\square\undefined
\def\square{\bigcirc
\errhelp={Anonymous ftp e-math.ams.com /ams/amsfonts}%
\errmessage{\string\square\space is an AMS symbol}%
\global\let\square\bigcirc}%
\fi
\global\let\check@pt@fm@thm\relax
}%
\fi
% Check for Paul.sty, which SERIOUSLY conflicts with this file.
% and also for version 2 or version 3 of commutative diagrams.
\def\check@pt@sty@v{%
\relax
\ifx\@@begintheorem\undefined
\else\message{*** QED.sty and the old Paul.sty seriously conflict! ***}%
\obsolete@pt@version{Paul.sty}%
\fi
\ifx\execHorizontalMap\undefined
\gdef\obsolete@pt@version##1{}% it's no longer needed
\else\global\let\di@gr@m\diagram
\gdef\diagram{\obsolete@pt@version{diagrams.tex}\di@gr@m}%
\fi
\global\let\check@pt@sty@v\relax
}%
%===========================================================================
% Define some standard ``theorem'' types.
\def\DefineStandardTheorems{%
%
% First set up uniform numbering in LaTeX;
% don't use this in plain TeX because this usage of \newcommand is not
% supported and we have already done by hand what it would do in LaTeX,
% viz to define the macro \theResult and the count \c@Result.
\relax\ifx\@@thm\undefined
\newtheorem{Result}{Result}[subsection]%
\@addtoreset{Result}{section}%
\ifx\chapter\undefined\else\@addtoreset{Result}{chapter}\fi
\fi
%
\let\theUnnumbered\relax\countdef\c@Unnumbered255 \def\p@Unnumbered{}%
\let\DefineStandardTheorems\relax
%
\newtheorem{Answer}[Result]{Answer}%
\newtheorem{Answers}[Result]{Answers}%
\newtheorem{Conjecture}[Result]{Conjecture}%
\newtheorem{Construction}[Result]{Construction}%
\newtheorem{Convention}[Unnumbered]{Convention}%
\newtheorem{Corollary}[Result]{Corollary}%
\newtheorem{Counterexample}[Result]{Counterexample}%
\newtheorem{Definition}[Result]{Definition}%
\newtheorem{Example}[Result]{Example}%
\newtheorem{Examples}[Result]{Examples}%
\newtheorem{Exercise}[Result]{Exercise}%
\newtheorem{Exercises}[Result]{Exercises}%
\newtheorem{Fact}[Result]{Fact}%
\newtheorem{Facts}[Result]{Facts}%
\newtheorem{Lemma}[Result]{Lemma}%
\newtheorem{NB}[Unnumbered]{NB}%
\newtheorem{Notation}[Result]{Notation}%
\newtheorem{Note}[Unnumbered]{Note}%
\newtheorem{Observation}[Result]{Observation}%
\newtheorem{Observations}[Result]{Observations}%
\newtheorem{Problem}[Result]{Problem}%
\newtheorem{Proposition}[Result]{Proposition}%
\newtheorem{PS}[Unnumbered]{PS}%
\newtheorem{Remark}[Result]{Remark}%
\newtheorem{Question}[Result]{Question}%
\newtheorem{Questions}[Result]{Questions}%
\newtheorem{Theorem}[Result]{Theorem}%
\newtheorem{Thesis}[Result]{Thesis}%
\newtheorem{Warning}[Result]{Warning}%
}
%===========================================================================
% Interaction with LaTeX2e (2 Jan 1994)
\ifx\newtheorem\undefined\else\ifx\ProvidesPackage\undefined
\message{^^J^^J}%
\message{****************************************************************}%
\message{! ***** You are using an obsolete implementation of LaTeX ******}%
\message{* A new version - called LaTeX2e - has been available from TeX *}%
\message{* FTP archives such as ftp.tex.ac.uk, ftp.uni-stuttgart.de and *}%
\message{* pip.shsu.edu since December 1993. It incorporates NFSS2 (the *}%
\message{* Mittelbach-Schoepf New Font Selection Scheme) but is reverse *}%
\message{* compatible with LaTeX versions 2.09 and is now the standard. *}%
\message{****************************************************************}%
\message{^^J^^J}%
\else
\ProvidesPackage{QED}[1996/06/24 right-justified end-of-proof mark]%
%\ProvidesFile{QED.sty}% I don't understand what this is for
\DeclareOption{roman-theorems}{\def\TheoremFont{\rm}}%
\DeclareOption{italic-theorems}{\def\TheoremFont{\it}}%
\DeclareOption{theorems-as-commands}{\TheoremsAsCommands}%
\DeclareOption{auto-QED}{\AutoQEDtrue}%
\DeclareOption{explicit-QED}{\AutoQEDfalse}%
\DeclareOption{number-theorems}{\NumberResultstrue}%
\DeclareOption{dont-number-theorems}{\NumberResultsfalse}%
\DeclareOption{black-square}{\def\qedsymbol{\blacksquare}}%
\DeclareOption{open-square}{\def\qedsymbol{\square}}%
\DeclareOption{define-standard-theorems}{\DefineStandardTheorems}%
\ProcessOptions
\fi\fi
%===========================================================================
% If Mittelbach's theorem.sty is loaded, skip the rest of the file.
\ifx\theorem@style\undefined\else\qedrestoreat\expandafter\endinput\fi
%===========================================================================
% Allow the user to suppress italicisation and numbering.
% The following two macros are called by LaTeX to begin a theorem
% respectively with and without an optional (``attribution'') argument.
% It is clear from latex.tex that they are intended to be customised.
% The code common to the two has been taken out as \begin@theorem and
% \TheoremHeader. Of these, the former is re-defined by \TheoremsAsCommands.
\def\@opargbegintheorem#1#2#3{\begin@theorem{\TheoremHeader{#1}{#2}{ (#3)} }}
\def\@begintheorem#1#2{\begin@theorem{\TheoremHeader{#1}{#2}{} }}
\def\begin@theorem#1{%
\trivlist\item[\hskip\labelsep {#1}]% % LaTeX likes this method.
\TheoremFont % Italicise the enunciation
\ifx\ProofFont\empty\def\ProofFont{\rm}\fi % but not any nested proof.
}%
%%% Here's what LaTeX (92/1/14) does:
%%%% RmS 91/08/14 Moved \it after \item to make it work with NFSS
%%\def\@begintheorem#1#2{\trivlist \item[\hskip \labelsep{\bf #1\ #2}]\it}
%%\def\@opargbegintheorem#1#2#3{\trivlist
%% \item[\hskip \labelsep{\bf #1\ #2\ (#3)}]\it}
%%\def\@endtheorem{\endtrivlist}
%===========================================================================
% If we're running under LaTeX, skip the rest of the file.
\ifx\newtheorem\undefined\else\qedrestoreat\expandafter\endinput\fi
%===========================================================================
% This implements a rudimentary version of \newtheorem for plain TeX.
% Only the unattributed theorems and the
% declarations \newtheorem{Theorem}[Result]{Theorem} and
% \newtheorem{Convention}[Unnumbered]{Convention} are supported.
% The numbering is based on the counts \chapternumber, \sectionnumber
% and \subsectionnumber, which it is up to you to define with \newcount.
% It's also up to you to reset \c@Result at the beginning of each section.
% Form the number: (chapter).(section).(subsection).(#1)
% where any of the first three parts which is zero
% negative or undefined is omitted.
\def\ther@sult#1{%
\ifx\chapternumber\undefined\else
\ifnum\chapternumber>0 \number\chapternumber.\fi\fi
\ifx\sectionnumber\undefined\else
\ifnum\sectionnumber>0 \number\sectionnumber.\fi\fi
\ifx\subsectionnumber\undefined\else
\ifnum\subsectionnumber>0 \number\subsectionnumber.\fi\fi
\expandafter\number\csname c@#1\endcsname}%
% plain version of LaTeX's \@thm
\def\plain@thm#1#2{% #1=counter, #2=text
\save@set@qed
\expandafter\advance\csname c@#1\endcsname1
\@begintheorem{#2}{\csname the#1\endcsname}%
}%
% Rudimentary \newtheorem
\def\newtheorem#1[#2]#3{% #1=command, #2=counter, #3=text
%
% \def\#1{\plain@thm{#2}{#3}}
\expandafter\def\csname #1\endcsname{\plain@thm{#2}{#3}}%
%
% \def\end#1{\@endtheorem}
\expandafter\def\csname end#1\endcsname{\@endtheorem}%
%
% if \c@#2 is not defined
% \newcount\c@#2
% \def\the#2{\ther@sult{#2}}
\expandafter\ifx\csname c@#2\endcsname\relax
\expandafter\expandafter\csname newcount\endcsname
\csname c@#2\endcsname
\expandafter\def\csname the#2\endcsname{\ther@sult{#2}}%
\fi
}%
\TheoremsAsCommands
\qedrestoreat\endinput
%===========================================================================
% BUGS
% \item\qed\end{letterlist} puts the square above the item label.
% ! You can't use `\unskip' in vertical mode.
% from \qed in a paragraph on its own.