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-%%
-%% This is file `amsthm.sty',
-%% generated with the docstrip utility.
-%%
-%% The original source files were:
-%%
-%% amsclass.dtx (with options: `amsthm')
-%%
-%%% ====================================================================
-%%% @LaTeX-file{
-%%% filename = "amsclass.dtx",
-%%% version = "2.20",
-%%% date = "2004/08/06",
-%%% time = "13:03:53 EDT",
-%%% checksum = "53558 5204 20497 185872",
-%%% author = "American Mathematical Society",
-%%% copyright = "Copyright 1995, 1999, 2004
-%%% 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,
-%%% Publications Technical Group,
-%%% 201 Charles Street,
-%%% Providence, RI 02904,
-%%% USA",
-%%% telephone = "401-455-4080 or (in the USA and Canada)
-%%% 800-321-4AMS (321-4267)",
-%%% FAX = "401-331-3842",
-%%% email = "tech-support@ams.org (Internet)",
-%%% codetable = "ISO/ASCII",
-%%% keywords = "latex, AMS, documentclass, theorem",
-%%% supported = "yes",
-%%% abstract = "This is the source for the amsthm package and three
-%%% AMS document classes: amsart, amsproc, and amsbook.
-%%% They are designed for use with LaTeX.",
-%%% 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.",
-%%% }
-%%% ====================================================================
-\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
-[1995/06/01]% LaTeX date must be June 1995 or later
-\ProvidesPackage{amsthm}[2004/08/06 v2.20]
-\let\@xp=\expandafter
-\let\@nx=\noexpand
-\def\@oparg#1[#2]{\@ifnextchar[{#1}{#1[#2]}}
-\long\def\@ifempty#1{\@xifempty#1@@..\@nil}
-\long\def\@xifempty#1#2@#3#4#5\@nil{%
- \ifx#3#4\@xp\@firstoftwo\else\@xp\@secondoftwo\fi}
-\long\def\@ifnotempty#1{\@ifempty{#1}{}}
-\def\setboxz@h{\setbox\z@\hbox}
-\def\@addpunct#1{%
- \relax\ifhmode
- \ifnum\spacefactor>\@m \else#1\fi
- \fi}
-\def\nopunct{\spacefactor 1007 }
-\def\frenchspacing{\sfcode`\.1006\sfcode`\?1005\sfcode`\!1004%
- \sfcode`\:1003\sfcode`\;1002\sfcode`\,1001 }
-\DeclareOption*{\input{\CurrentOption .thm}}
-\ProcessOptions
-
-\newcommand{\theoremstyle}[1]{%
- \@ifundefined{th@#1}{%
- \PackageWarning{amsthm}{Unknown theoremstyle `#1'}%
- \thm@style{plain}%
- }{%
- \thm@style{#1}%
- }%
-}
-\newtoks\thm@style
-\thm@style{plain}
-\newtoks\thm@bodyfont \thm@bodyfont{\itshape}
-\newtoks\thm@headfont \thm@headfont{\bfseries}
-\newtoks\thm@notefont \thm@notefont{}
-\newtoks\thm@headpunct \thm@headpunct{.}
-\newskip\thm@preskip \newskip\thm@postskip
-\def\thm@space@setup{%
- \thm@preskip=\topsep \thm@postskip=\thm@preskip
-}
-\renewcommand{\newtheorem}{\@ifstar{\@xnthm *}{\@xnthm \relax}}
-\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\thm@style\endcsname}%
- {}{##1}}}%
- \else % numbered theorem, need to check for optional arg
- \def\@tempa{\@oparg{\@ynthm{#2}}[]}%
- \fi
- }%
- \@tempa
-}
-\def\@ynthm#1[#2]#3{%
- \ifx\relax#2\relax
- \def\@tempa{\@oparg{\@xthm{#1}{#3}}[]}%
- \else
- \@ifundefined{c@#2}{%
- \def\@tempa{\@nocounterr{#2}}%
- }{%
- \@xp\xdef\csname the#1\endcsname{\@xp\@nx\csname the#2\endcsname}%
- \toks@{#3}%
- \@xp\xdef\csname#1\endcsname{%
- \@nx\@thm{%
- \let\@nx\thm@swap
- \if S\thm@swap\@nx\@firstoftwo\else\@nx\@gobble\fi
- \@xp\@nx\csname th@\the\thm@style\endcsname}%
- {#2}{\the\toks@}}%
- \let\@tempa\relax
- }%
- \fi
- \@tempa
-}
-\def\@xthm#1#2[#3]{%
- \ifx\relax#3\relax
- \newcounter{#1}%
- \else
- \newcounter{#1}[#3]%
- \@xp\xdef\csname the#1\endcsname{\@xp\@nx\csname the#3\endcsname
- \@thmcountersep\@thmcounter{#1}}%
- \fi
- \toks@{#2}%
- \@xp\xdef\csname#1\endcsname{%
- \@nx\@thm{%
- \let\@nx\thm@swap
- \if S\thm@swap\@nx\@firstoftwo\else\@nx\@gobble\fi
- \@xp\@nx\csname th@\the\thm@style\endcsname}%
- {#1}{\the\toks@}}%
-}
-\def\@thm#1#2#3{%
- \ifhmode\unskip\unskip\par\fi
- \normalfont
- \trivlist
- \let\thmheadnl\relax
- \let\thm@swap\@gobble
- \thm@notefont{\fontseries\mddefault\upshape}%
- \thm@headpunct{.}% add period after heading
- \thm@headsep 5\p@ plus\p@ minus\p@\relax
- \thm@space@setup
- #1% style overrides
- \@topsep \thm@preskip % used by thm head
- \@topsepadd \thm@postskip % 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
-}
-\def\@restorelabelsep{\relax}
-\let\@ythm\relax
-\let\thmname\@iden \let\thmnote\@iden \let\thmnumber\@iden
-\providecommand\@upn{\textup}
-\def\thmhead@plain#1#2#3{%
- \thmname{#1}\thmnumber{\@ifnotempty{#1}{ }\@upn{#2}}%
- \thmnote{ {\the\thm@notefont(#3)}}}
-\let\thmhead\thmhead@plain
-\def\swappedhead#1#2#3{%
- \thmnumber{#2}%
- \thmname{\@ifnotempty{#2}{~}#1}%
- \thmnote{ {\the\thm@notefont(#3)}}}
-\let\swappedhead@plain=\swappedhead
-\let\thmheadnl\relax
-\let\thm@indent\noindent
-\let\thm@swap\@gobble
-\def\@begintheorem#1#2[#3]{%
- \deferred@thm@head{\the\thm@headfont \thm@indent
- \@ifempty{#1}{\let\thmname\@gobble}{\let\thmname\@iden}%
- \@ifempty{#2}{\let\thmnumber\@gobble}{\let\thmnumber\@iden}%
- \@ifempty{#3}{\let\thmnote\@gobble}{\let\thmnote\@iden}%
- \thm@swap\swappedhead\thmhead{#1}{#2}{#3}%
- \the\thm@headpunct
- \thmheadnl % possibly a newline.
- \hskip\thm@headsep
- }%
- \ignorespaces}
-\newskip\thm@headsep
-\thm@headsep=5pt plus1pt minus1pt\relax
-\let\adjust@parskip@nobreak=\@nbitem
-\newtoks\dth@everypar
-\dth@everypar={%
- \@minipagefalse \global\@newlistfalse
- \@noparitemfalse
- \if@inlabel
- \global\@inlabelfalse
- \begingroup \setbox\z@\lastbox
- \ifvoid\z@ \kern-\itemindent \fi
- \endgroup
- \unhbox\@labels
- \fi
- \if@nobreak \@nobreakfalse \clubpenalty\@M
- \else \clubpenalty\@clubpenalty \everypar{}%
- \fi
-}%
-\def\deferred@thm@head#1{%
- \if@inlabel \indent \par \fi % eject a section head if one is pending
- \if@nobreak
- \adjust@parskip@nobreak
- \else
- \addpenalty\@beginparpenalty
- \addvspace\@topsep
- \addvspace{-\parskip}%
- \fi
- \global\@inlabeltrue
- \everypar\dth@everypar
- \sbox\@labels{\normalfont#1}%
- \ignorespaces
-}
-\def\nonslanted{\relax
- \@xp\let\@xp\@tempa\csname\f@shape shape\endcsname
- \ifx\@tempa\itshape\upshape
- \else\ifx\@tempa\slshape\upshape\fi\fi}
-\def\swapnumbers{\edef\thm@swap{\if S\thm@swap N\else S\fi}}
-\def\thm@swap{N}%
-\let\@opargbegintheorem\relax
-\def\th@plain{%
-%% \let\thm@indent\noindent % no indent
-%% \thm@headfont{\bfseries}% heading font is bold
-%% \thm@notefont{}% same as heading font
-%% \thm@headpunct{.}% add period after heading
-%% \let\thm@swap\@gobble
-%% \thm@preskip\topsep
-%% \thm@postskip\theorempreskipamount
- \itshape % body font
-}
-\def\th@definition{%
- \normalfont % body font
-}
-\def\th@remark{%
- \thm@headfont{\itshape}%
- \normalfont % body font
- \thm@preskip\topsep \divide\thm@preskip\tw@
- \thm@postskip\thm@preskip
-}
-\def\@endtheorem{\endtrivlist\@endpefalse }
-\newcommand{\newtheoremstyle}[9]{%
- \@ifempty{#5}{\dimen@\z@skip}{\dimen@#5\relax}%
- \ifdim\dimen@=\z@
- \toks@{#4\let\thm@indent\noindent}%
- \else
- \toks@{#4\def\thm@indent{\noindent\hbox to#5{}}}%
- \fi
- \def\@tempa{#8}\ifx\space\@tempa
- \toks@\@xp{\the\toks@ \thm@headsep\fontdimen\tw@\font\relax}%
- \else
- \def\@tempb{\newline}%
- \ifx\@tempb\@tempa
- \toks@\@xp{\the\toks@ \thm@headsep\z@skip
- \def\thmheadnl{\newline}}%
- \else
- \toks@\@xp{\the\toks@ \thm@headsep#8\relax}%
- \fi
- \fi
- \begingroup
- \thm@space@setup
- \@defaultunits\@tempskipa#2\thm@preskip\relax\@nnil
- \@defaultunits\@tempskipb#3\thm@postskip\relax\@nnil
- \xdef\@gtempa{\thm@preskip\the\@tempskipa
- \thm@postskip\the\@tempskipb\relax}%
- \endgroup
- \@temptokena\@xp{\@gtempa
- \thm@headfont{#6}\thm@headpunct{#7}%
- }%
- \@ifempty{#9}{%
- \let\thmhead\thmhead@plain
- }{%
- \@namedef{thmhead@#1}##1##2##3{#9}%
- \@temptokena\@xp{\the\@temptokena
- \@xp\let\@xp\thmhead\csname thmhead@#1\endcsname}%
- }%
- \@xp\xdef\csname th@#1\endcsname{\the\toks@ \the\@temptokena}%
-}
-\DeclareRobustCommand{\qed}{%
- \ifmmode \mathqed
- \else
- \leavevmode\unskip\penalty9999 \hbox{}\nobreak\hfill
- \quad\hbox{\qedsymbol}%
- \fi
-}
-\let\QED@stack\@empty
-\let\qed@elt\relax
-\newcommand{\pushQED}[1]{%
- \toks@{\qed@elt{#1}}\@temptokena\expandafter{\QED@stack}%
- \xdef\QED@stack{\the\toks@\the\@temptokena}%
-}
-\newcommand{\popQED}{%
- \begingroup\let\qed@elt\popQED@elt \QED@stack\relax\relax\endgroup
-}
-\def\popQED@elt#1#2\relax{#1\gdef\QED@stack{#2}}
-\newcommand{\qedhere}{%
- \begingroup \let\mathqed\math@qedhere
- \let\qed@elt\setQED@elt \QED@stack\relax\relax \endgroup
-}
-\newif\ifmeasuring@
-\newif\iffirstchoice@ \firstchoice@true
-\def\setQED@elt#1#2\relax{%
- \ifmeasuring@
- \else \iffirstchoice@ \gdef\QED@stack{\qed@elt{}#2}\fi
- \fi
- #1%
-}
-\def\qed@warning{%
- \PackageWarning{amsthm}{The \@nx\qedhere command may not work
- correctly here}%
-}
-\newcommand{\mathqed}{\quad\hbox{\qedsymbol}}
-\def\linebox@qed{\hfil\hbox{\qedsymbol}\hfilneg}
-\@ifpackageloaded{amsmath}{%
- \def\math@qedhere{%
- \@ifundefined{\@currenvir @qed}{%
- \qed@warning\quad\hbox{\qedsymbol}%
- }{%
- \@xp\aftergroup\csname\@currenvir @qed\endcsname
- }%
- }
- \def\displaymath@qed{%
- \relax
- \ifmmode
- \ifinner \aftergroup\linebox@qed
- \else
- \eqno
- \let\eqno\relax \let\leqno\relax \let\veqno\relax
- \hbox{\qedsymbol}%
- \fi
- \else
- \aftergroup\linebox@qed
- \fi
- }
- \@xp\let\csname equation*@qed\endcsname\displaymath@qed
- \def\equation@qed{%
- \iftagsleft@
- \hbox{\phantom{\quad\qedsymbol}}%
- \gdef\alt@tag{%
- \rlap{\hbox to\displaywidth{\hfil\qedsymbol}}%
- \global\let\alt@tag\@empty
- }%
- \else
- \gdef\alt@tag{%
- \global\let\alt@tag\@empty
- \vtop{\ialign{\hfil####\cr
- \tagform@\theequation\cr
- \qedsymbol\cr}}%
- \setbox\z@
- }%
- \fi
- }
- \def\qed@tag{%
- \global\tag@true \nonumber
- &\omit\setboxz@h {\strut@ \qedsymbol}\tagsleft@false
- \place@tag@gather
- \kern-\tabskip
- \ifst@rred \else \global\@eqnswtrue \fi \global\advance\row@\@ne \cr
- }
- \def\split@qed{%
- \def\endsplit{\crcr\egroup \egroup \ctagsplit@false \rendsplit@
- \aftergroup\align@qed
- }%
- }
- \def\align@qed{%
- \ifmeasuring@ \tag*{\qedsymbol}%
- \else \let\math@cr@@@\qed@tag
- \fi
- }
- \@xp\let\csname align*@qed\endcsname\align@qed
- \@xp\let\csname gather*@qed\endcsname\align@qed
-%% Needs some patching up for amsmath 1.2
-}{% end of amsmath branch, start plain LaTeX branch
- \def\math@qedhere{%
- \@ifundefined{\@currenvir @qed}{%
- \qed@warning \aftergroup\displaymath@qed
- }{%
- \@xp\aftergroup\csname\@currenvir @qed\endcsname
- }%
- }
- \def\displaymath@qed{%
- \relax
- \ifmmode
- \ifinner \aftergroup\aftergroup\aftergroup\linebox@qed
- \else
- \eqno \def\@badmath{$$}%
- \let\eqno\relax \let\leqno\relax \let\veqno\relax
- \hbox{\qedsymbol}%
- \fi
- \else
- \aftergroup\linebox@qed
- \fi
- }
- \@ifundefined{ver@leqno.clo}{%
- \def\equation@qed{\displaymath@qed \quad}%
- }{%
- \def\equation@qed{\displaymath@qed}%
- }
- \def\@tempa#1$#2#3\@nil{%
- \def\[{#1$#2\def\@currenvir{displaymath}#3}%
- }%
- \expandafter\@tempa\[\@nil
-}
-\@ifpackageloaded{amstex}{%
- \def\@tempa{TT}%
-}{%
- \@ifpackageloaded{amsmath}{%
- \def\@tempb#1 v#2.#3\@nil{#2}%
- \ifnum\@xp\@xp\@xp\@tempb\csname ver@amsmath.sty\endcsname v0.0\@nil
- <\tw@
- \def\@tempa{TT}%
- \else
- \def\@tempa{TF}%
- \fi
- }{%
- \def\@tempa{TF}
- }%
-}
-\if\@tempa
- \renewcommand{\math@qedhere}{\quad\hbox{\qedsymbol}}%
-\fi
-\newcommand{\openbox}{\leavevmode
- \hbox to.77778em{%
- \hfil\vrule
- \vbox to.675em{\hrule width.6em\vfil\hrule}%
- \vrule\hfil}}
-\DeclareRobustCommand{\textsquare}{%
- \begingroup \usefont{U}{msa}{m}{n}\thr@@\endgroup
-}
-\providecommand{\qedsymbol}{\openbox}
-\newenvironment{proof}[1][\proofname]{\par
- \pushQED{\qed}%
- \normalfont \topsep6\p@\@plus6\p@\relax
- \trivlist
- \item[\hskip\labelsep
- \itshape
- #1\@addpunct{.}]\ignorespaces
-}{%
- \popQED\endtrivlist\@endpefalse
-}
-\providecommand{\proofname}{Proof}
-\endinput
-%%
-%% End of file `amsthm.sty'.