%%% ====================================================================
%%%  @LaTeX-file{
%%%     filename        = "amsthm.dtx",
%%%     version         = "1.2beta",
%%%     date            = "1994/10/27",
%%%     time            = "11:25:13 EDT",
%%%     author          = "American Mathematical Society",
%%%     copyright       = "Copyright (C) 1994 American Mathematical Society,
%%%                        all rights reserved.  Copying of this file is
%%%                        authorized only if either:
%%%                        (1) you make absolutely no changes to your copy,
%%%                        including name; OR
%%%                        (2) if you do make changes, you first rename it
%%%                        to some other name.",
%%%     address         = "American Mathematical Society,
%%%                        Technical Support,
%%%                        Electronic Products and Services,
%%%                        P. O. Box 6248,
%%%                        Providence, RI 02940,
%%%                        USA",
%%%     telephone       = "401-455-4080 or (in the USA and Canada)
%%%                        800-321-4AMS (321-4267)",
%%%     FAX             = "401-331-3842",
%%%     checksum        = "01388 549 2338 19979",
%%%     email           = "tech-support@math.ams.org (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "latex, amslatex, ams-latex, theorem",
%%%     supported       = "yes",
%%%     abstract        = "This is part of the AMS-\LaTeX{} distribution.
%%%                        It is a package which provides multiple
%%%                        theorem styles, unnumbered theorem types, and
%%%                        a proof environment with automatic ending
%%%                        Q.E.D. symbol. Loosely derived from
%%%                        Mittelbach's theorem.sty.",
%%%     docstring       = "The checksum field above contains a CRC-16
%%%                        checksum as the first value, followed by the
%%%                        equivalent of the standard UNIX wc (word
%%%                        count) utility output of lines, words, and
%%%                        characters.  This is produced by Robert
%%%                        Solovay's checksum utility.",
%%%  }
%%% ====================================================================
% \iffalse
%    The following section of code makes this file self-printable.
%    \begin{macrocode}
%<*driver>
\NeedsTeXFormat{LaTeX2e}
\documentclass{amsdtx}
\begin{document}
\title{The \pkg{amsthm} package}
\author{American Mathematical Society\\Michael Downes}
\date{Version \fileversion, \filedate}
\hDocInput{amsthm.dtx}
\end{document}
%</driver>
%    \end{macrocode}
% \fi
%
% \maketitle
% \section{Introduction}
%    The \pkg{amsthm} package is loosely derived from \fn{theorem.sty}
%    version 2.1c; it adds \cn{newtheorem*} for unnumbered environments
%    and changes the extensibility support for loading extra theorem
%    styles from external files: now it is done through the package
%    option mechanism.
%
%    Here are some examples showing the kinds of theorem environment
%    declarations that are possible with the \pkg{amsthm} package.
% \begin{verbatim}
% \newtheorem{prop}{Proposition}
% \newtheorem{thm}{Theorem}[section]
% \newtheorem{lem}[thm]{Lemma}
% \newtheorem*{Zorn}{Zorn's Lemma}
%
% \theoremstyle{definition}
% \newtheorem{dfn}{Definition}
%
% \theoremstyle{remark}
% \newtheorem*{rmk}{Remark}
% \end{verbatim}
%
%    The first four statements all define environments using the default
%    theorem style (`plain'), since there is no prefatory
%    \cn{theoremstyle} declaration.
%    The first statement defines an automatically numbered \env{prop}
%    environment whose headings will look like this: Proposition 1,
%    Proposition 2, and so forth. The second statement
%    defines an environment \env{thm} with
%    numbers subordinate to section numbers, so the headings will look
%    like this: Theorem 1.1, Theorem 1.2, Theorem 1.3, \dots, (in
%    section 2:) Theorem 2.1, Theorem 2.2, and so forth. The third
%    statement defines a \env{lem} environment whose numbers
%    will interleave in sequence with the theorem numbers: Theorem 1.3,
%    Lemma 1.4, Lemma 1.5, Theorem 1.6, and so forth. The fourth
%    statement defines a special unnumbered lemma named `Zorn's Lemma'.
%    The remaining two \cn{newtheorem} statements have no special
%    features except for the \cn{theoremstyle} declarations that cause
%    them to use different styles.
%
%    There are three basic styles provided: The `plain' style produces
%    bold headings and italic text; the `definition' style produces bold
%    headings and roman text; the `remark' style produces italic
%    headings and roman text. Other theorem styles can be provided by
%    putting a suitable definition in a separate file whose name ends
%    with \fn{.thm}. For example, suppose that you wanted to make a
%    theorem style `exercise' for exercises. Create a file called
%    \fn{exercise.thm} and in it define a command \cs{th@exercise}
%    following the form of the commands \cs{th@plain},
%    \cs{th@definition}, \cs{th@remark} given below. Then to use the
%    new style, write
% \begin{verbatim}
% \usepackage[exercise]{amsthm}
% ...
% \theoremstyle{exercise}
% \end{verbatim}
%
% \StopEventually{}
%
% \section{Implementation}
%    Standard declaration of package name and date.
%    \begin{macrocode}
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{amsthm}[1994/10/27 v1.2beta]
%    \end{macrocode}
%
%    Load some utility functions from \pkg{amsgen} if it is not already
%    loaded. Can't use \cn{RequirePackage} because of the later
%    \cn{ProcessOptions} command, and can't put this after the
%    \cn{ProcessOptions} command because we might need some bits for
%    processing a \fn{.thm} file.
%    \begin{macrocode}
\@ifl@aded{sty}{amsgen}{}{\input{amsgen.sty}}
%    \end{macrocode}
%
%    The \cn{theoremstyle} command is very simple except for the need to
%    warn about an unknown theoremstyle.
%    \begin{macrocode}
\newcommand{\theoremstyle}[1]{%
  \@ifundefined{th@#1}{%
    \PackageWarning{amsthm}{%
      Unknown theoremstyle `#1'. Using `plain'}%
    \theorem@style{plain}%
  }{%
    \theorem@style{#1}%
  }%
}
%    \end{macrocode}
%
%    \begin{macrocode}
\newtoks\theorem@style
\theorem@style{plain}
%    \end{macrocode}
%
%    This code for handling theorem body and header font is a
%    simplification of the code in Mittelbach's \fn{theorem} package.
%    For consistency we make the header punctuation a token register as
%    well. And we add a separate font specification for the optional
%    note (since in AMS publications the note usually takes a different
%    font). The \cs{normalfont} that in Mittelbach's code resided here
%    is transferred to \cs{@thm}.
%    \begin{macrocode}
\newtoks\theorembodyfont
\theorembodyfont{\itshape}
\newtoks\theoremheadfont
\theoremheadfont{\bfseries}
\newtoks\theoremnotefont
\theoremnotefont{\bfseries}
\newtoks\theoremheadpunct
\theoremheadpunct{.}
\newskip\theorempreskipamount
\newskip\theorempostskipamount
%    \end{macrocode}
%    Modify \cn{newtheorem} to add |*| option. If a |*| is found, pass
%    it on to \cs{@xnthm} as the first argument. Otherwise pass a dummy
%    first arg of \cs{relax}.
%    \begin{macrocode}
\renewcommand{\newtheorem}{\@ifstar{\@xnthm *}{\@xnthm \relax}}
%    \end{macrocode}
%
%    Check to see if an optional arg is present after the first
%    mandatory arg (which is \arg{2} at the moment since the |*| or
%    non-|*| is \arg{1}).
%    \begin{macrocode}
\def\@xnthm#1#2{%
  \let\@tempa\relax
  \@xp\@ifdefinable\csname #2\endcsname{%
    \global\@xp\let\csname end#2\endcsname\@endtheorem
    \ifx *#1% unnumbered, need to get one more mandatory arg
      \edef\@tempa##1{%
        \gdef\@xp\@nx\csname#2\endcsname{%
          \@nx\@thm{\@xp\@nx\csname th@\the\theorem@style\endcsname}%
            {}{##1}}}%
    \else % numbered theorem, need to check for optional arg
      \def\@tempa{\@oparg{\@ynthm{#2}}[]}%
    \fi
  }%
  \@tempa
}
%    \end{macrocode}
%
%    Environment numbered together with a previously defined
%    environment.
%
%    Arg1: env name, e.g. `thm'\par
%    Arg2: optional sibling counter\par
%    Arg3: heading text e.g. `Theorem'
%    \begin{macrocode}
\def\@ynthm#1[#2]#3{%
%    \end{macrocode}
%    If optional arg \arg{2} is empty, call \cs{@xthm} to look for a
%    possible optional arg in terminal position. Note that
%    the two optional args are mutually exclusive.
%    \begin{macrocode}
  \@ifempty{#2}{%
    \@oparg{\@xthm{#1}{#3}}[]%
  }{%
    \@ifundefined{c@#2}{%
      \@nocounterr{#2}%
    }{%
      \@xp\xdef\csname the#1\endcsname{\@xp\@nx\csname the#2\endcsname}%
      \toks@{#3}%
      \@xp\xdef\csname#1\endcsname{%
        \@nx\@thm{\@xp\@nx\csname th@\the\theorem@style\endcsname}%
            {#2}{\the\toks@}}%
    }%
  }%
}
%    \end{macrocode}
%
%    Environment numbered relative to the counter given as \arg{3}. This
%    function should really be named \cs{@znthm} but we're trying to
%    save a bit of hash table and string pool by reusing one of the
%    command names rendered obsolete by the amsthm option.
%
%    Arg1: env name e.g. `thm';
%    Arg2: heading text e.g. `Theorem';
%    Arg3: parent counter e.g. section.
%    \begin{macrocode}
\def\@xthm#1#2[#3]{%
%    \end{macrocode}
%    Set up the counter \verb'c@#1' and optionally add it to the reset
%    list of counter \arg{3}.
%    \begin{macrocode}
  \@ifempty{#3}{%
    \newcounter{#1}%
  }{%
    \newcounter{#1}[#3]%
%    \end{macrocode}
%    Define \cn{thexxx} to be \verb'\theyyy.\arabic{xxx}' (assuming
%    default values of punctuation and numbering style). The use of
%    \cs{xdef} here is inherited from the old \LaTeX{} code, I'm not
%    sure it's a good idea in general, but there should not be any
%    problems unless someone changes the value of \cs{@thmcounter} or
%    \cs{@thmcounter}.
%    \begin{macrocode}
    \@xp\xdef\csname the#1\endcsname{\@xp\@nx\csname the#3\endcsname
      \@thmcountersep\@thmcounter{#1}}%
  }%
  \toks@{#2}%
  \@xp\xdef\csname#1\endcsname{%
    \@nx\@thm{\@xp\@nx\csname th@\the\theorem@style\endcsname}%
      {#1}{\the\toks@}}%
}
%    \end{macrocode}
%
%    If arg \arg{2} is empty, this is an unnumbered environment;
%    otherwise \arg{2} is the name of a counter. \arg{3} is descriptive
%    name such as ``Theorem'' or ``Lemma''. Arg \arg{1} is the style
%    function, for example \cs{th@plain}.
%    \begin{macrocode}
\def\@thm#1#2#3{\normalfont
  \trivlist
  \labelsep.5em\relax
%    \end{macrocode}
%    Explicitly set plain style here, then override parts as necessary
%    in the function provided as \arg{1}.
%    \begin{macrocode}
  \let\theoremindent\noindent % no indent
  \let\theorem@swap\@nonswapped
  \theoremheadfont{\bfseries}% heading font bold
  \theoremnotefont\@emptytoks% default to header font
  \theoremheadpunct{.}% add period after heading
  \theorempreskipamount1\baselineskip\@plus.2\baselineskip
                                    \@minus.2\baselineskip
  \theorempostskipamount\theorempreskipamount
  #1% style overrides
  \@topsep \theorempreskipamount               % used by first \item
  \@topsepadd \theorempostskipamount           % used by \@endparenv
  \def\@tempa{#2}\ifx\@empty\@tempa
    \def\@tempa{\@oparg{\@begintheorem{#3}{}}[]}%
  \else
    \refstepcounter{#2}%
    \def\@tempa{\@oparg{\@begintheorem{#3}{\csname the#2\endcsname}}[]}%
  \fi
  \@tempa
}
%    \end{macrocode}
%
%    This variation of the \cs{@thm} command is no longer needed. The
%    variation \cs{@xthm} was commandeered for \cn{newtheorem} use.
%    \begin{macrocode}
\let\@ythm\relax
%    \end{macrocode}
%
%    If argument \arg{2} is empty, then this is an unnumbered
%    environment. Otherwise \arg{2} is a numbering command such as
%    \cn{thexyz}.
%    \begin{macrocode}
\def\@begintheorem#1#2[#3]{%
  \item[\normalfont % reset in case body font is abnormal
%    \end{macrocode}
%    The standard weird compensation for labelsep space inside an
%    \cn{item} that is not a normal user-level \cn{item}:
%    \begin{macrocode}
  \hskip\labelsep
  \the\theoremheadfont
  \theoremindent
%    \end{macrocode}
%    The \cs{theorem@swap} function might be changed under some
%    circumstances to swap the position of the heading text and the
%    number.
%    \begin{macrocode}
  \theorem@swap{#1}{#2}%
%    \end{macrocode}
%    If there is an optional note for the theorem head, add it here.
%    Note that this part is not localized to a group, so the final
%    punctuation (if present) will match the font of the theorem note
%    (if a note is present).
%    \begin{macrocode}
  \@ifnotempty{#3}{\space\the\theoremnotefont(#3\unskip)}%
%    \end{macrocode}
%    I can't think of any example where the after-head punctuation
%    should be omitted so it seems correct not to use \cs{@addpunct}
%    here.
%    \begin{macrocode}
  \the\theoremheadpunct]%
  \ignorespaces}
%    \end{macrocode}
%
%  \begin{macro}{\nonslanted}
%    The \cn{nonslanted} command changes the current font to
%    \cn{upshape} if it is \cn{itshape} or \cn{slshape}. This is used
%    for document structure numbers that should be consistently upright
%    in all contexts.
%    \begin{macrocode}
\def\nonslanted{\relax
  \ifx\f@shape\itdefault\upshape
  \else\ifx\f@shape\sldefault\upshape\fi\fi}
%    \end{macrocode}
%  \end{macro}
%
%  \begin{macro}{\@nonswapped}
%    The default value of \cs{theorem@swap} is nonswapped.
%    \begin{macrocode}
\def\@nonswapped#1#2{#1\@ifnotempty{#2}{\enskip{\nonslanted#2}\unskip}}%
%    \end{macrocode}
%  \end{macro}
%
%  \begin{macro}{\@swapped}
%    The amsart documentclass uses a different default definition of
%    \cs{@swapped} that also does some font changes and uses a different
%    horizontal space.
%    \begin{macrocode}
\def\@swapped#1#2{%
  {\nonslanted#2}\@ifnotempty{#1}{\@addpunct{.}\enskip#1\unskip}}
%    \end{macrocode}
%  \end{macro}
%
%  \begin{macro}{\theorem@swap}
%    This function could be changed by the \cn{swapnumbers} command.
%    Default is \cs{@nonswapped}.
%    \begin{macrocode}
\let\theorem@swap=\@nonswapped
%    \end{macrocode}
%  \end{macro}
%
%  \begin{macro}{\swapnumbers}
%    The command \verb'\swapnumbers{thm,prop,defn,...}' causes all the
%    given environments to have the numbers swapped to the front.
%    \begin{macrocode}
\def\swapnumbers#1{\PackageError{amsthm}{Command \nx@\swapnumbers not
  ready yet}}
%    \end{macrocode}
%  \end{macro}
%
%    \cs{@opargbegintheorem} not needed, \cs{@oparg} utility serves
%    instead.
%    \begin{macrocode}
\let\@opargbegintheorem\relax
%    \end{macrocode}
%
%    The default style of `plain', all except the body font, is built
%    into the \cs{@thm} macro to ensure that nested environments work
%    properly. So the \cs{th@plain} macro can just give the body font.
%    \begin{macrocode}
\def\th@plain{%
%%\let\theoremindent\noindent % no indent
%%\let\theorem@swap\@nonswapped % don't swap number to the left
%%\theoremheadfont{\bfseries}% heading font is bold
%%\theoremnotefont{}% same as heading font
%%\theoremheadpunct{.}% add period after heading
%%\theorempreskipamount\baselineskip\@plus.2\baselineskip
%%  \@minus.2\baselineskip
%%\theorempostskipamount\theorempreskipamount
  \itshape % body font
}
%    \end{macrocode}
%
%    Theorem style `definition' is the same as `plain' except for the
%    body font.
%    \begin{macrocode}
\def\th@definition{%
  \normalfont % body font
}
%    \end{macrocode}
%
%    Theorem style `remark' differs from `plain' in head font and  body
%    font.
%    \begin{macrocode}
\def\th@remark{%
  \theoremheadfont{\itshape}%
  \normalfont % body font
}
%    \end{macrocode}
%
%    The standard definition of \cs{@endtheorem} is just
%    \cs{endtrivlist}, but that doesn't automatically start a new
%    paragraph, so we add \cs{@endpefalse} in order to ensure a new
%    paragraph.
%    \begin{macrocode}
\def\@endtheorem{\endtrivlist\@endpefalse }
%    \end{macrocode}
%
%  \begin{macro}{\newtheoremstyle}
%    An easy way to make a not too complicated variant theorem style.
%    Usage:
% \begin{verbatim}
% \newtheoremstyle{NAME}%
%   {INDENT}{SWAP}{HEADFONT}{NOTEFONT}{PUNCT}{BODYFONT}%
%   {ABOVESPACE}{BELOWSPACE}
% \end{verbatim}
%    Values for INDENT are empty=yes or `no'; values for SWAP are
%    empty=no or 's'. Other values are accepted as given.
%    \begin{macrocode}
\newcommand{\newtheoremstyle}[9]{%
  \@xp\ifx\csname#2indent\endcsname\noindent
    \toks@{\let\theoremindent\noindent}%
  \else
    \toks@{\let\theoremindent\indent}%
  \fi
  \ifx s#3%
    \@temptokena{\let\theorem@swap\@swapped}%
  \else
    \@temptokena{\let\theorem@swap\@nonswapped}%
  \fi
  \theoremheadfont{\theoremheadfont{#4}%
    \theoremnotefont{#5}\theoremheadpunct{#6}%
    \theorempreskipamount#8\relax
    \theorempostskipamount#9\relax
    #7% body font
  }%
  \@xp\xdef\csname th@#1\endcsname{%
    \the\toks@ \the\@temptokena \the\theoremheadfont}%
}
%    \end{macrocode}
%  \end{macro}
%
%
%  \begin{macro}{\qed}
%    Define \cn{qed} for end of proof. This command should \emph{not}
%    ever occur in inner math mode (i.e. |$...$| at paragraph level) but
%    it might be used in a displayed equation.
%    \begin{macrocode}
\DeclareRobustCommand{\qed}{%
  \ifmmode % do nothing extra
  \else \leavevmode\unskip\penalty9999 \hbox{}\nobreak\hfill
  \fi
%    \end{macrocode}
%    The hbox is to prevent a line break within the \cn{qedsymbol} if it
%    is defined to be something composite--- e.g., things like
%    \verb"(Corollary 1.2) \openbox" as are occasionally done.
%    \begin{macrocode}
  \quad\hbox{\qedsymbol}}
%    \end{macrocode}
%  \end{macro}
%
%    The reason that we do not simply use the \cn{square} symbol from
%    msam for the open-box qed symbol is that we want to avoid requiring
%    users to have the AMSFonts font package. And the \fn{lasy} \cn{Box}
%    is too large.
%    \begin{macrocode}
\newcommand{\openbox}{\leavevmode
  \hbox to.77778em{%
  \hfil\vrule
  \vbox to.675em{\hrule width.6em\vfil\hrule}%
  \vrule\hfil}}
\newcommand{\qedsymbol}{\openbox}
%    \end{macrocode}
%
%    The proof environment is never numbered, and has a \cn{qed} at the
%    end, which makes it inconvenient to use \cn{newtheorem} for
%    defining it. Also authors frequently need to substitute an
%    alternative heading text (e.g. `Proof of the Dilation Lemma')
%    instead of the default `Proof'. For all these reasons we define the
%    proof environment here instead of leaving it for authors to define.
%    \begin{macrocode}
\newenvironment{proof}[1][\proofname]{\par
  \normalfont
  \topsep6\p@\@plus6\p@ \trivlist
  \item[\hskip\labelsep\itshape
    #1\@addpunct{.}]\ignorespaces
}{%
  \qed\endtrivlist
}
%    \end{macrocode}
%    Default for \cn{proofname}:
%    \begin{macrocode}
\newcommand{\proofname}{Proof}
%    \end{macrocode}
%
%    Any option given in the \cn{usepackage} statement will be treated
%    as the name of a file containing additional theorem style
%    definitions.
%    \begin{macrocode}
\DeclareOption*{\input{\CurrentOption .thm}}
\ProcessOptions
%    \end{macrocode}
%
%    For reference:
% \begin{verbatim}
% From: tycchow@math.mit.edu (Timothy Y. Chow)
% Subject: Suppressing theorem numbering in LaTeX
% Message-ID: <1994Aug11.234754.22523@galois.mit.edu>
% Date: Thu, 11 Aug 94 23:47:54 GMT
% To: tex-news@SHSU.EDU
%
% A friend of mine wants numbering of theorems, conjectures, and so on
% suppressed if there is only one of them in his article.  In other words
% he wants "Conjecture 1" to appear as simply "Conjecture" if there is no
% Conjecture 2.  What is the best way to go about doing this?
% ...
% \end{verbatim}
%
%    The usual \cs{endinput} to ensure that random garbage at the end of
%    the file doesn't get copied by \fn{docstrip}.
%    \begin{macrocode}
\endinput
%    \end{macrocode}
%
% \CheckSum{377}
% \Finale