% RESOURCEamspptSimple ; 
 % Assumes AmSTeX(version2) loaded, but NOT AmSppt.sty
 % These macros are intentionally simple minded and have
 % simple syntax; this permits easy alteration (TeX macros are usually
 % very devious).  Don't hesitate to make alterations,
 % but in that case rename this file!

 %%% avoid double input

 %avoid double input
 \bgroup
 \catcode`\!=12 
 \ifx\RESOURCEams\relax 
   \immediate\write16{}%
   \message{ !!! RESOURCEams macros already defined !!!}
   \gdef\RESOURCEams{\endinput}%
  \else \global\let\RESOURCEams\relax
  \fi 
 \egroup
 \RESOURCEams

 \catcode`\@=11

 %%% The following macros will make you call upon auxiliary files
 %% when needed.
 \bgroup
 \catcode`\!=12 
 \gdef\Acc{%\show\Acc%
   \errmessage{ !!! You need to input RESOURCEamsAcc.tex !!!}\end
   }
 \gdef\amsCD{%
   \errmessage{ !!! You need to input  RESOURCEamsCD.tex !!!}\end
   }
 \gdef\gLinefigure{%
   \errmessage{ !!! You need to input RESOURCEfig.tex !!!}\end
   }
  \egroup

 %%% Font macros
 %%

 \def\Bf#1{{\bf#1}}

  \def \Bi #1{{\bi{#1}\unskip\/}}

 \def \Admin #1{\begingroup\mathsurround=0 pt
  \leavevmode%p222-3: \hskip -\lastskip for \unskip 
  \ifmmode\hbox{$\roman{{#1}}$}\else$\roman{{#1}}$\fi
  \endgroup }%{{}} prevents misinterpretation of naked numbers

 %%% Logical formatting
 %%

 \font \titlefont=cmbx10 scaled 1200
 \long\def\Title#1\endTitle{\heading\titlefont#1\endheading}

\long\def\Author#1\endAuthor{\heading\smc #1\endheading}

\def\Subheading{\medskip\goodbreak\subheading}
\let\SubheadingA\Subheading
\let\SubheadingB\Subheading
\let\SubheadingC\Subheading

 \let \Theorem\proclaim
  \let \endTheorem\endproclaim
 
 %\let\Proof\demo  %% make substitution by hand 
 %\let\endProof\enddemo

 \def\Proof{\medskip\goodbreak\noindent
    \hbox{\it Proof.\kern 1em}\ignorespaces}
 
  %% A Box for the Quod est demonstrandum:
  \def\qedbox{\hbox{\vbox{
    \hrule width0.2cm height0.2pt
    \hbox to 0.2cm{\vrule height 0.2cm width 0.2pt
             \hfil\vrule height0.2cm width 0.2pt}
    \hrule width0.2cm height 0.2pt}\kern1pt}}

  %% Typing in \qed makes the qedbox right justified:
  \def\qed{\ifmmode\qedbox
    \else\unskip\ \hglue0mm\hfill\qedbox\medskip
     \goodbreak\fi}

 \def \Remark#1{\medskip \goodbreak\par\noindent{\smc  #1.}}
 \def \endRemark{\medskip \goodbreak}

 \def \Example#1{\Remark {#1}}
 \def \endExample{\medskip \goodbreak}

 \def \Definition#1{\Remark {#1}}
 \def \endDefinition{\medskip \goodbreak}

 \def\ItemStyle{\bold}%
 \def \Item #1{\smallskip
    \ifhmode\else\nointerlineskip\fi
    {\parskip=4pt\noindent
    \hbox{$\def\let\relax\let\bf\relax\ItemStyle{{#1}}$}\enskip}}

 \def \Itemitem #1{\itemitem{\hbox{$\def\let\relax\let\bf\relax%
                                \ItemStyle{#1}$}}}

 \def \Benchmark { }
 \def \References#1{\begingroup \leftskip=25 pt \parskip=4 pt plus 2 pt
    \goodbreak \hbox to 1 pt{} \vskip 15 pt plus 10 pt minus 5 pt
 \centerline{\bf #1}
 \frenchspacing \def \Benchmark{\Refmark }
 \def \Refmark##1\cite ##2{%
       \par\noindent \llap{\null\cite{##2}\quad}\kern 0pt}
 \nobreak\vskip 8pt \nobreak}

 \def \endReferences {~\unskip\par\endgroup \medskip\goodbreak }

 \def \Footnote #1#2{\plainfootnote{#1}{#2}} 

 %Symbols macros

 \def \preXbox{\hbox{$
  \vcenter{\hbox{
    \vrule\vbox to 6.7 pt{
      \hrule \vfil \hbox to 12 pt{
        \hfil}%
      \vfil\hrule}%
    \vrule}}\hskip 4pt%
  $}}

 \def \Xbox{\raise -.25pt\hbox{\preXbox}}

 \def \Nonsense {{~\unskip \kern-3.5 pt %
    \hbox{\mathsurround=0 pt\Xbox \kern -16.5 pt $>\kern-3pt<$}}}

 \def \Blackbox
   {\leavevmode\hskip .3pt \vbox{\hrule height 6.9pt
     \hbox{\hskip 4.5pt}}\hskip .5pt}%

 \def \<{{$\mathsurround= 0 pt\raise 1.4
        pt\hbox{$\scriptscriptstyle 
       \langle \kern -1 pt \langle\hskip 2 pt $}$}}
 
 \def \>{{\mathsurround= 0 pt$\hskip 2 pt \raise 1.4
           pt\hbox{$\scriptscriptstyle 
           \rangle \kern -1 pt \rangle$}$}} 

 \def \Matrix #1{\matrix#1\endmatrix} 

 \def \amsMatrix #1\endamsMatrix{\matrix#1\endmatrix} 

 \def\amsCases #1\endamsCases{\cases#1\endcases}

 \def\tagform@#1{\hbox{\rm\Pretag\ignorespaces#1\unskip\Posttag}}
 \def\Pretag{(}
 \def\Posttag{)}

 \def\Eqno #1$${\def\Pretag{}\def\Posttag{}
      \tag"\Admin{#1}"$$}

 \def \Multline#1\endMultline#2$${\def\Pretag{}\def\Posttag{}
    \def\Eqno{}\multline#1\endmultline\tag"\Admin{#2\hbox to 1sp{}}"$$} 

 \def \bigMidvert{\kern4pt \big \vert \kern4pt}

 \def \Midvert{\kern3pt \vert \kern3pt}

 \def \Sharp {\mathord{\#}}

 \def \bigConnectedsum {\mathop{\#}\limits}

 \def \Coprod {\mathop{\raise 1.2pt \hbox{$\coprod$}}\limits}

 \def \Lim {\lim\limits}

 \def \Lbrack {{$[\![$}}

 \def \Rbrack {{$]\!]$}}

 %%% Binomial coef trick macros mentioned in Sweet-teX manual (rare)
 %%
 \def \Rparen {\right ) }
 \def \Lparen {\futurelet\next \Lptaupe}
 \def\Lptaupe{\ifx \next ^ \let\this\LLparen 
  \else \let\this\LLLparen  \fi\this} 
 \def\LLparen {\left ( \Atop }
 \def \Atop ^#1_#2{{#1\atop#2}}
 \def\LLLparen {\left (}

 %%%%%%%%%%%%%%%%  Accents were here

 \def \circleover #1{\overset\circ\to {#1}}

 \def \Cdot{\mathbin{\raise .4 ex \hbox to 3pt {\hss\bf .\hss}}}

 \def \llonguparrow{\bigg\uparrow }

 \def \llongdownarrow{\bigg\downarrow}

 \def \llongrightarrow{\kern 1pt\mathop
      {\kern0pt\longrightarrow\kern1pt}\limits}

 \def \llongleftarrow{\kern-2pt\mathop
      {\kern3pt\longleftarrow\kern3pt}\limits}
 
 \def \llongtwoheadrarrow {\kern-2pt
  \mathop{\kern3pt\longrightarrow \kern-14pt 
  \longrightarrow\kern3pt}\limits}

 \def \llongleftrightarrow {\kern-2pt
  \mathop{\kern3pt\longleftrightarrow\kern3pt}\limits}

 \def \llongmapsto {\kern-2pt
  \mathop{\kern3pt\longmapsto\kern3pt}\limits}


 %%%%%%%%%%%%%%%%% CD macros were here

 \def\Trademark{\hbox{\Admin{{}^{\scriptscriptstyle TM}}}}

 \def \AmS{{\textfontii A}\kern -.1667em\lower .5ex\hbox {\textfontii
 M}\kern -.125em{\textfontii S}}

 \def\LaTeX{{\rm L\kern-.36em\raise.3ex\hbox{\smc a}\kern-.15em
   \TeX}}

 \def\Undef{\Nonsense }

 %The following correspond to rare Sweet-teX symbols, 
 %and will produce a X'ed box on your TeX printout 
 %until something better is devised
 \def\Bigasterisk{\Undef}
 \def\Control{\Undef}
 \def\llongrightarrowtail{\Undef}
 \def\llongswarrow{\Undef }
 \def\llongsearrow{\Undef }
 \def\llongnwarrow{\Undef }
 \def\llongnearrow{\Undef }
 \def\llongtwoheadrightarrow{\mathbin
        {{\longrightarrow} \kern -1850\mu {\rightarrow}}}

 \def \Longeq {\mathop{=\kern-5pt=}\limits } 

%%%% 4 lines in case cmex pointsizes missing
 \font\eightex=cmex10 at 8pt     \skewchar\eightex='60 
 \font\sevenex=cmex10 at 7pt      \skewchar\sevenex='60   
 \font\sixex=cmex10 at 6pt      \skewchar\sixex='60   
 \tenpoint

 \catcode`\@=13 %active