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+%%
+%% This is file `amssymb.sty',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% amssymb.dtx
+%%
+%%% ====================================================================
+%%% @LaTeX-file{
+%%% filename = "amssymb.dtx",
+%%% version = "2.2d",
+%%% date = "2002/01/22",
+%%% time = "10:06:53 EST",
+%%% checksum = "51146 363 1168 18275",
+%%% author = "American Mathematical Society",
+%%% copyright = "Copyright 2001 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,
+%%% 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",
+%%% email = "tech-support@ams.org (Internet)",
+%%% codetable = "ISO/ASCII",
+%%% keywords = "latex, amslatex, ams-latex, math symbol,
+%%% amsfonts, msam, msbm",
+%%% supported = "yes",
+%%% abstract = "This file is part of the AMSFonts distribution.
+%%% It is a \LaTeX{} package that defines symbol
+%%% names for all the math symbols in the fonts
+%%% MSAM and MSBM, of the AMSFonts (2.0+) collection.",
+%%% 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)
+[1994/12/01]% LaTeX date must be December 1994 or later
+\ProvidesPackage{amssymb}[2002/01/22 v2.2d]
+\DeclareOption{psamsfonts}{\PassOptionsToPackage{psamsfonts}{amsfonts}}
+\ProcessOptions\relax
+\RequirePackage{amsfonts}[1995/01/01]
+\let\square\relax \let\rightsquigarrow\square \let\lozenge\square
+\let\vartriangleright\square \let\vartriangleleft\square
+\let\trianglerighteq\square \let\trianglelefteq\square
+\begingroup \catcode`\"=12
+\DeclareMathSymbol{\boxdot} {\mathbin}{AMSa}{"00}
+\DeclareMathSymbol{\boxplus} {\mathbin}{AMSa}{"01}
+\DeclareMathSymbol{\boxtimes} {\mathbin}{AMSa}{"02}
+\DeclareMathSymbol{\square} {\mathord}{AMSa}{"03}
+\DeclareMathSymbol{\blacksquare} {\mathord}{AMSa}{"04}
+\DeclareMathSymbol{\centerdot} {\mathbin}{AMSa}{"05}
+\DeclareMathSymbol{\lozenge} {\mathord}{AMSa}{"06}
+\DeclareMathSymbol{\blacklozenge} {\mathord}{AMSa}{"07}
+\DeclareMathSymbol{\circlearrowright} {\mathrel}{AMSa}{"08}
+\DeclareMathSymbol{\circlearrowleft} {\mathrel}{AMSa}{"09}
+%% In amsfonts.sty:
+%%\DeclareMathSymbol{\rightleftharpoons}{\mathrel}{AMSa}{"0A}
+\DeclareMathSymbol{\leftrightharpoons} {\mathrel}{AMSa}{"0B}
+\DeclareMathSymbol{\boxminus} {\mathbin}{AMSa}{"0C}
+\DeclareMathSymbol{\Vdash} {\mathrel}{AMSa}{"0D}
+\DeclareMathSymbol{\Vvdash} {\mathrel}{AMSa}{"0E}
+\DeclareMathSymbol{\vDash} {\mathrel}{AMSa}{"0F}
+\DeclareMathSymbol{\twoheadrightarrow} {\mathrel}{AMSa}{"10}
+\DeclareMathSymbol{\twoheadleftarrow} {\mathrel}{AMSa}{"11}
+\DeclareMathSymbol{\leftleftarrows} {\mathrel}{AMSa}{"12}
+\DeclareMathSymbol{\rightrightarrows} {\mathrel}{AMSa}{"13}
+\DeclareMathSymbol{\upuparrows} {\mathrel}{AMSa}{"14}
+\DeclareMathSymbol{\downdownarrows} {\mathrel}{AMSa}{"15}
+\DeclareMathSymbol{\upharpoonright} {\mathrel}{AMSa}{"16}
+ \global\let\restriction\upharpoonright
+\DeclareMathSymbol{\downharpoonright} {\mathrel}{AMSa}{"17}
+\DeclareMathSymbol{\upharpoonleft} {\mathrel}{AMSa}{"18}
+\DeclareMathSymbol{\downharpoonleft}{\mathrel}{AMSa}{"19}
+\DeclareMathSymbol{\rightarrowtail} {\mathrel}{AMSa}{"1A}
+\DeclareMathSymbol{\leftarrowtail} {\mathrel}{AMSa}{"1B}
+\DeclareMathSymbol{\leftrightarrows}{\mathrel}{AMSa}{"1C}
+\DeclareMathSymbol{\rightleftarrows}{\mathrel}{AMSa}{"1D}
+\DeclareMathSymbol{\Lsh} {\mathrel}{AMSa}{"1E}
+\DeclareMathSymbol{\Rsh} {\mathrel}{AMSa}{"1F}
+\DeclareMathSymbol{\rightsquigarrow} {\mathrel}{AMSa}{"20}
+\DeclareMathSymbol{\leftrightsquigarrow}{\mathrel}{AMSa}{"21}
+\DeclareMathSymbol{\looparrowleft} {\mathrel}{AMSa}{"22}
+\DeclareMathSymbol{\looparrowright} {\mathrel}{AMSa}{"23}
+\DeclareMathSymbol{\circeq} {\mathrel}{AMSa}{"24}
+\DeclareMathSymbol{\succsim} {\mathrel}{AMSa}{"25}
+\DeclareMathSymbol{\gtrsim} {\mathrel}{AMSa}{"26}
+\DeclareMathSymbol{\gtrapprox} {\mathrel}{AMSa}{"27}
+\DeclareMathSymbol{\multimap} {\mathrel}{AMSa}{"28}
+\DeclareMathSymbol{\therefore} {\mathrel}{AMSa}{"29}
+\DeclareMathSymbol{\because} {\mathrel}{AMSa}{"2A}
+\DeclareMathSymbol{\doteqdot} {\mathrel}{AMSa}{"2B}
+ \global\let\Doteq\doteqdot
+\DeclareMathSymbol{\triangleq} {\mathrel}{AMSa}{"2C}
+\DeclareMathSymbol{\precsim} {\mathrel}{AMSa}{"2D}
+\DeclareMathSymbol{\lesssim} {\mathrel}{AMSa}{"2E}
+\DeclareMathSymbol{\lessapprox} {\mathrel}{AMSa}{"2F}
+\DeclareMathSymbol{\eqslantless} {\mathrel}{AMSa}{"30}
+\DeclareMathSymbol{\eqslantgtr} {\mathrel}{AMSa}{"31}
+\DeclareMathSymbol{\curlyeqprec} {\mathrel}{AMSa}{"32}
+\DeclareMathSymbol{\curlyeqsucc} {\mathrel}{AMSa}{"33}
+\DeclareMathSymbol{\preccurlyeq} {\mathrel}{AMSa}{"34}
+\DeclareMathSymbol{\leqq} {\mathrel}{AMSa}{"35}
+\DeclareMathSymbol{\leqslant} {\mathrel}{AMSa}{"36}
+\DeclareMathSymbol{\lessgtr} {\mathrel}{AMSa}{"37}
+\DeclareMathSymbol{\backprime} {\mathord}{AMSa}{"38}
+\DeclareMathSymbol{\risingdotseq} {\mathrel}{AMSa}{"3A}
+\DeclareMathSymbol{\fallingdotseq}{\mathrel}{AMSa}{"3B}
+\DeclareMathSymbol{\succcurlyeq} {\mathrel}{AMSa}{"3C}
+\DeclareMathSymbol{\geqq} {\mathrel}{AMSa}{"3D}
+\DeclareMathSymbol{\geqslant} {\mathrel}{AMSa}{"3E}
+\DeclareMathSymbol{\gtrless} {\mathrel}{AMSa}{"3F}
+%% in amsfonts.sty
+%% \DeclareMathSymbol{\sqsubset} {\mathrel}{AMSa}{"40}
+%% \DeclareMathSymbol{\sqsupset} {\mathrel}{AMSa}{"41}
+\DeclareMathSymbol{\vartriangleright}{\mathrel}{AMSa}{"42}
+\DeclareMathSymbol{\vartriangleleft} {\mathrel}{AMSa}{"43}
+\DeclareMathSymbol{\trianglerighteq} {\mathrel}{AMSa}{"44}
+\DeclareMathSymbol{\trianglelefteq} {\mathrel}{AMSa}{"45}
+\DeclareMathSymbol{\bigstar} {\mathord}{AMSa}{"46}
+\DeclareMathSymbol{\between} {\mathrel}{AMSa}{"47}
+\DeclareMathSymbol{\blacktriangledown} {\mathord}{AMSa}{"48}
+\DeclareMathSymbol{\blacktriangleright} {\mathrel}{AMSa}{"49}
+\DeclareMathSymbol{\blacktriangleleft} {\mathrel}{AMSa}{"4A}
+\DeclareMathSymbol{\vartriangle} {\mathrel}{AMSa}{"4D}
+\DeclareMathSymbol{\blacktriangle} {\mathord}{AMSa}{"4E}
+\DeclareMathSymbol{\triangledown} {\mathord}{AMSa}{"4F}
+\DeclareMathSymbol{\eqcirc} {\mathrel}{AMSa}{"50}
+\DeclareMathSymbol{\lesseqgtr} {\mathrel}{AMSa}{"51}
+\DeclareMathSymbol{\gtreqless} {\mathrel}{AMSa}{"52}
+\DeclareMathSymbol{\lesseqqgtr} {\mathrel}{AMSa}{"53}
+\DeclareMathSymbol{\gtreqqless} {\mathrel}{AMSa}{"54}
+\DeclareMathSymbol{\Rrightarrow} {\mathrel}{AMSa}{"56}
+\DeclareMathSymbol{\Lleftarrow} {\mathrel}{AMSa}{"57}
+\DeclareMathSymbol{\veebar} {\mathbin}{AMSa}{"59}
+\DeclareMathSymbol{\barwedge} {\mathbin}{AMSa}{"5A}
+\DeclareMathSymbol{\doublebarwedge} {\mathbin}{AMSa}{"5B}
+%% In amsfonts.sty
+%%\DeclareMathSymbol{\angle} {\mathord}{AMSa}{"5C}
+\DeclareMathSymbol{\measuredangle} {\mathord}{AMSa}{"5D}
+\DeclareMathSymbol{\sphericalangle} {\mathord}{AMSa}{"5E}
+\DeclareMathSymbol{\varpropto} {\mathrel}{AMSa}{"5F}
+\DeclareMathSymbol{\smallsmile} {\mathrel}{AMSa}{"60}
+\DeclareMathSymbol{\smallfrown} {\mathrel}{AMSa}{"61}
+\DeclareMathSymbol{\Subset} {\mathrel}{AMSa}{"62}
+\DeclareMathSymbol{\Supset} {\mathrel}{AMSa}{"63}
+\DeclareMathSymbol{\Cup} {\mathbin}{AMSa}{"64}
+ \global\let\doublecup\Cup
+\DeclareMathSymbol{\Cap} {\mathbin}{AMSa}{"65}
+ \global\let\doublecap\Cap
+\DeclareMathSymbol{\curlywedge} {\mathbin}{AMSa}{"66}
+\DeclareMathSymbol{\curlyvee} {\mathbin}{AMSa}{"67}
+\DeclareMathSymbol{\leftthreetimes} {\mathbin}{AMSa}{"68}
+\DeclareMathSymbol{\rightthreetimes}{\mathbin}{AMSa}{"69}
+\DeclareMathSymbol{\subseteqq} {\mathrel}{AMSa}{"6A}
+\DeclareMathSymbol{\supseteqq} {\mathrel}{AMSa}{"6B}
+\DeclareMathSymbol{\bumpeq} {\mathrel}{AMSa}{"6C}
+\DeclareMathSymbol{\Bumpeq} {\mathrel}{AMSa}{"6D}
+\DeclareMathSymbol{\lll} {\mathrel}{AMSa}{"6E}
+ \global\let\llless\lll
+\DeclareMathSymbol{\ggg} {\mathrel}{AMSa}{"6F}
+ \global\let\gggtr\ggg
+\DeclareMathSymbol{\circledS} {\mathord}{AMSa}{"73}
+\DeclareMathSymbol{\pitchfork} {\mathrel}{AMSa}{"74}
+\DeclareMathSymbol{\dotplus} {\mathbin}{AMSa}{"75}
+\DeclareMathSymbol{\backsim} {\mathrel}{AMSa}{"76}
+\DeclareMathSymbol{\backsimeq} {\mathrel}{AMSa}{"77}
+\DeclareMathSymbol{\complement} {\mathord}{AMSa}{"7B}
+\DeclareMathSymbol{\intercal} {\mathbin}{AMSa}{"7C}
+\DeclareMathSymbol{\circledcirc} {\mathbin}{AMSa}{"7D}
+\DeclareMathSymbol{\circledast} {\mathbin}{AMSa}{"7E}
+\DeclareMathSymbol{\circleddash} {\mathbin}{AMSa}{"7F}
+%% Begin AMSb declarations
+\DeclareMathSymbol{\lvertneqq} {\mathrel}{AMSb}{"00}
+\DeclareMathSymbol{\gvertneqq} {\mathrel}{AMSb}{"01}
+\DeclareMathSymbol{\nleq} {\mathrel}{AMSb}{"02}
+\DeclareMathSymbol{\ngeq} {\mathrel}{AMSb}{"03}
+\DeclareMathSymbol{\nless} {\mathrel}{AMSb}{"04}
+\DeclareMathSymbol{\ngtr} {\mathrel}{AMSb}{"05}
+\DeclareMathSymbol{\nprec} {\mathrel}{AMSb}{"06}
+\DeclareMathSymbol{\nsucc} {\mathrel}{AMSb}{"07}
+\DeclareMathSymbol{\lneqq} {\mathrel}{AMSb}{"08}
+\DeclareMathSymbol{\gneqq} {\mathrel}{AMSb}{"09}
+\DeclareMathSymbol{\nleqslant} {\mathrel}{AMSb}{"0A}
+\DeclareMathSymbol{\ngeqslant} {\mathrel}{AMSb}{"0B}
+\DeclareMathSymbol{\lneq} {\mathrel}{AMSb}{"0C}
+\DeclareMathSymbol{\gneq} {\mathrel}{AMSb}{"0D}
+\DeclareMathSymbol{\npreceq} {\mathrel}{AMSb}{"0E}
+\DeclareMathSymbol{\nsucceq} {\mathrel}{AMSb}{"0F}
+\DeclareMathSymbol{\precnsim} {\mathrel}{AMSb}{"10}
+\DeclareMathSymbol{\succnsim} {\mathrel}{AMSb}{"11}
+\DeclareMathSymbol{\lnsim} {\mathrel}{AMSb}{"12}
+\DeclareMathSymbol{\gnsim} {\mathrel}{AMSb}{"13}
+\DeclareMathSymbol{\nleqq} {\mathrel}{AMSb}{"14}
+\DeclareMathSymbol{\ngeqq} {\mathrel}{AMSb}{"15}
+\DeclareMathSymbol{\precneqq} {\mathrel}{AMSb}{"16}
+\DeclareMathSymbol{\succneqq} {\mathrel}{AMSb}{"17}
+\DeclareMathSymbol{\precnapprox} {\mathrel}{AMSb}{"18}
+\DeclareMathSymbol{\succnapprox} {\mathrel}{AMSb}{"19}
+\DeclareMathSymbol{\lnapprox} {\mathrel}{AMSb}{"1A}
+\DeclareMathSymbol{\gnapprox} {\mathrel}{AMSb}{"1B}
+\DeclareMathSymbol{\nsim} {\mathrel}{AMSb}{"1C}
+\DeclareMathSymbol{\ncong} {\mathrel}{AMSb}{"1D}
+\DeclareMathSymbol{\diagup} {\mathord}{AMSb}{"1E}
+\DeclareMathSymbol{\diagdown} {\mathord}{AMSb}{"1F}
+\DeclareMathSymbol{\varsubsetneq} {\mathrel}{AMSb}{"20}
+\DeclareMathSymbol{\varsupsetneq} {\mathrel}{AMSb}{"21}
+\DeclareMathSymbol{\nsubseteqq} {\mathrel}{AMSb}{"22}
+\DeclareMathSymbol{\nsupseteqq} {\mathrel}{AMSb}{"23}
+\DeclareMathSymbol{\subsetneqq} {\mathrel}{AMSb}{"24}
+\DeclareMathSymbol{\supsetneqq} {\mathrel}{AMSb}{"25}
+\DeclareMathSymbol{\varsubsetneqq} {\mathrel}{AMSb}{"26}
+\DeclareMathSymbol{\varsupsetneqq} {\mathrel}{AMSb}{"27}
+\DeclareMathSymbol{\subsetneq} {\mathrel}{AMSb}{"28}
+\DeclareMathSymbol{\supsetneq} {\mathrel}{AMSb}{"29}
+\DeclareMathSymbol{\nsubseteq} {\mathrel}{AMSb}{"2A}
+\DeclareMathSymbol{\nsupseteq} {\mathrel}{AMSb}{"2B}
+\DeclareMathSymbol{\nparallel} {\mathrel}{AMSb}{"2C}
+\DeclareMathSymbol{\nmid} {\mathrel}{AMSb}{"2D}
+\DeclareMathSymbol{\nshortmid} {\mathrel}{AMSb}{"2E}
+\DeclareMathSymbol{\nshortparallel} {\mathrel}{AMSb}{"2F}
+\DeclareMathSymbol{\nvdash} {\mathrel}{AMSb}{"30}
+\DeclareMathSymbol{\nVdash} {\mathrel}{AMSb}{"31}
+\DeclareMathSymbol{\nvDash} {\mathrel}{AMSb}{"32}
+\DeclareMathSymbol{\nVDash} {\mathrel}{AMSb}{"33}
+\DeclareMathSymbol{\ntrianglerighteq}{\mathrel}{AMSb}{"34}
+\DeclareMathSymbol{\ntrianglelefteq}{\mathrel}{AMSb}{"35}
+\DeclareMathSymbol{\ntriangleleft} {\mathrel}{AMSb}{"36}
+\DeclareMathSymbol{\ntriangleright} {\mathrel}{AMSb}{"37}
+\DeclareMathSymbol{\nleftarrow} {\mathrel}{AMSb}{"38}
+\DeclareMathSymbol{\nrightarrow} {\mathrel}{AMSb}{"39}
+\DeclareMathSymbol{\nLeftarrow} {\mathrel}{AMSb}{"3A}
+\DeclareMathSymbol{\nRightarrow} {\mathrel}{AMSb}{"3B}
+\DeclareMathSymbol{\nLeftrightarrow}{\mathrel}{AMSb}{"3C}
+\DeclareMathSymbol{\nleftrightarrow}{\mathrel}{AMSb}{"3D}
+\DeclareMathSymbol{\divideontimes} {\mathbin}{AMSb}{"3E}
+\DeclareMathSymbol{\varnothing} {\mathord}{AMSb}{"3F}
+\DeclareMathSymbol{\nexists} {\mathord}{AMSb}{"40}
+\DeclareMathSymbol{\Finv} {\mathord}{AMSb}{"60}
+\DeclareMathSymbol{\Game} {\mathord}{AMSb}{"61}
+%% In amsfonts.sty:
+%%\DeclareMathSymbol{\mho} {\mathord}{AMSb}{"66}
+\DeclareMathSymbol{\eth} {\mathord}{AMSb}{"67}
+\DeclareMathSymbol{\eqsim} {\mathrel}{AMSb}{"68}
+\DeclareMathSymbol{\beth} {\mathord}{AMSb}{"69}
+\DeclareMathSymbol{\gimel} {\mathord}{AMSb}{"6A}
+\DeclareMathSymbol{\daleth} {\mathord}{AMSb}{"6B}
+\DeclareMathSymbol{\lessdot} {\mathbin}{AMSb}{"6C}
+\DeclareMathSymbol{\gtrdot} {\mathbin}{AMSb}{"6D}
+\DeclareMathSymbol{\ltimes} {\mathbin}{AMSb}{"6E}
+\DeclareMathSymbol{\rtimes} {\mathbin}{AMSb}{"6F}
+\DeclareMathSymbol{\shortmid} {\mathrel}{AMSb}{"70}
+\DeclareMathSymbol{\shortparallel} {\mathrel}{AMSb}{"71}
+\DeclareMathSymbol{\smallsetminus} {\mathbin}{AMSb}{"72}
+\DeclareMathSymbol{\thicksim} {\mathrel}{AMSb}{"73}
+\DeclareMathSymbol{\thickapprox} {\mathrel}{AMSb}{"74}
+\DeclareMathSymbol{\approxeq} {\mathrel}{AMSb}{"75}
+\DeclareMathSymbol{\succapprox} {\mathrel}{AMSb}{"76}
+\DeclareMathSymbol{\precapprox} {\mathrel}{AMSb}{"77}
+\DeclareMathSymbol{\curvearrowleft} {\mathrel}{AMSb}{"78}
+\DeclareMathSymbol{\curvearrowright}{\mathrel}{AMSb}{"79}
+\DeclareMathSymbol{\digamma} {\mathord}{AMSb}{"7A}
+\DeclareMathSymbol{\varkappa} {\mathord}{AMSb}{"7B}
+\DeclareMathSymbol{\Bbbk} {\mathord}{AMSb}{"7C}
+\DeclareMathSymbol{\hslash} {\mathord}{AMSb}{"7D}
+%% In amsfonts.sty:
+%%\DeclareMathSymbol{\hbar} {\mathord}{AMSb}{"7E}
+\DeclareMathSymbol{\backepsilon} {\mathrel}{AMSb}{"7F}
+\endgroup
+\endinput
+%%
+%% End of file `amssymb.sty'.