% pproof.sty for LaTeX 2.09 -- Released 18 Mar 1996 
% modified for use with Latex 2e and amsmath package 13 Nov 2007 
% Copyright (C) 1996, 2007 by Phillip E. Parker  phil@math.wichita.edu 
%
% This style defines the proof environment. Use it by calling \begin{proof} 
% and finish with \end{proof}. Calling it with \begin{proof}[name] allows 
% the inclusion of an optional name; in this it is similar to the theorem 
% environment. \eop may be called separately before \end{proof} without 
% conflict; e.g., inside display math. In each case, \Box is put at the 
% right margin, below an equation number if present. This style also 
% modifies the equation, eqnarray, and eqnarray* environments so that one 
% can call \eop on the last line to mark the end of a proof.
\typeout{Proof environment by Phil Parker < 13 Nov 2007  >}
%\makeatletter % Uncomment to use in a preamble.
 
% For convenience, there is a separate end-of-proof symbol \eops. It takes 
% an optional argument to control how much it is lowered; the default is 
% 1.25ex. Positive amounts raise it and negative ones lower it more. You 
% must place it _exactly_ where you want it. 
\def\eops{\@ifnextchar[{\@opargeops}{\@eops}}
\newlength{\@ptemp}

\def\@opargeops[#1]{\setlength{\@ptemp}{1.25ex}%
\addtolength{\@ptemp}{-#1}\lower\@ptemp\hbox{$\Box$}}

\def\@eops{\lower 1.25ex\hbox{$\Box$}}
% These conditionals control when to place an \eops (all initially false).
\global\newif\ifeopmark
\global\newif\ifeqn 
\global\newif\ifproof
\global\newif\ifproofended 
% \eop either places an \eops appropriately, or sets a flag for later use, 
% when called inside a proof environment. Since some "invisible" commands
% (such as \label) may produce visible space, call \eop _last_.
\def\eop{\ifproofended
\else\leavevmode\ifproof\global\proofendedtrue\fi
\ifhmode\unskip\nobreak\hfil\penalty 50 
   \hskip.4em\hbox{}\nobreak\hfil\eops[.5ex]
   \parfillskip=0pt \finalhyphendemerits=0
\else\ifmmode\ifinner\global\eopmarktrue
\else\ifeqn\global\eopmarktrue
\else\eqno{\eops}\fi\fi\fi\fi\fi}
% This defines the proof environment. 
\def\proof{\prooftrue\proofendedfalse\@ifnextchar[{\@opargproof}{\@proof}}
\def\endproof{\eop\end{trivlist}\global\proofendedfalse}

\def\@opargproof[#1]{\begin{trivlist}%
\item[]{\bf Proof (#1):\, }}
\let\end@opargproof=\endproof

\def\@proof{\begin{trivlist}%
\item[]{\bf Proof:\, }}
\let\end@proof=\endproof
% Next, the modified equation which can mark the end of a proof with an 
% appropriately placed \eops. Use by placing \eop just before
% \end{equation}.
% This does not work with 2e and amsmath now. PEP 13 Nov 2007 
%\let\oldequation=\equation
%\def\equation{\eqntrue\oldequation}
%\def\endequation{\ifeopmark\eqno % This must be changed now. PEP
%   \hbox{\@eqnnum}\makebox[0pt][r]{\eops[-1.75ex]}%
%   \else\eqno\hbox{\@eqnnum}\fi$$
%\global\@ignoretrue\global\eopmarkfalse
%\ifproof\else\global\proofendedfalse\fi}

% Next, the modified eqnarray which can end a proof similarly. Use by 
% placing \eop just before \end{eqnarray}. 
\def\endeqnarray{\let\@tempa\relax
   \ifcase\@eqcnt \def\@tempa{& & &}\or \def\@tempa{& &}%
   \else \def\@tempa{&}\fi \@tempa 
\if@eqnsw\@eqnnum\ifeopmark\makebox[0pt][r]{\eops[-1.75ex]}\fi
   \stepcounter{equation}\else\ifeopmark\makebox[0pt][r]{\eops}\fi\fi
\global\@eqnswtrue\global\@eqcnt\z@\cr\egroup 
\global\advance\c@equation\m@ne$$\global\@ignoretrue
\global\eopmarkfalse\ifproof\else\global\proofendedfalse\fi}
% Finally, the modified eqnarray* which can end a proof similarly. Use by 
% placing \eop just before \end{eqnarray*}. 
\@namedef{endeqnarray*}{\let\@tempa\relax
   \ifcase\@eqcnt \def\@tempa{& & &}\or \def\@tempa{& &}%
   \else \def\@tempa{&}\fi \@tempa 
\if@eqnsw\ifeopmark\makebox[0pt][r]{\eops}\fi\fi
\global\@eqnswtrue\global\@eqcnt\z@\cr\egroup
\global\advance\c@equation\m@ne$$\global\@ignoretrue
\global\eopmarkfalse\ifproof\else\global\proofendedfalse\fi}
%\makeatother % Uncomment to use in a preamble. 
\endinput % Comment out to use in a preamble.