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%=====================================================================================================================================
% Package akkmathproof by Igor Akkerman (c) 2000, 2001, 2002, 2003, 2004, 2005
% Package providing utilities for typesetting mathematical proofs.
%
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License (latest version).
%
% The latest version of this license can be found at
% http://www.latex-project.org/lppl.txt
%
% This file may only be distributed together with the full 'AkkTeX' bundle.
%=====================================================================================================================================
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
\ProvidesPackage{akkmathproof}[2005/04/30 1.2.0 by Igor Akkerman (c) 2000, 2001, 2002, 2003, 2004, 2005 Package providing utilities for typesetting mathematical proofs]
%=====================================================================================================================================
\RequirePackage{ifthen}
\makeatletter
%------------------------------------------------------------------------------
% Universal proof utilities
%------------------------------------------------------------------------------
\newcommand \akk@prooflabel {Proof}
\newcommand \prooflabel[1] {\renewcommand \akk@prooflabel {#1}}
\newcommand \proofendsymbol {\ensuremath{\Box}}
\newboolean{proofended}
\newcommand \proofend {%
\ifbool{mmode}{%
\tag*{\proofendsymbol}%
}{%
\hspace*{\fill}\proofendsymbol%
}%
\global\proofendedtrue%
}
\newenvironment{proof}{%
\unskip\par%
\textit{\textbf{\akk@prooflabel:}}\\%
\begin{proof*}%
}{%
\end{proof*}%
\par%
}
\newenvironment{Proof}{%
\unskip\par%
\textit{\textbf{\akk@prooflabel:}}%
\begin{proof*}%
}{%
\end{proof*}%
\par%
}
\newenvironment{proof*}{%
\setboolean{proofended}{false}%
}{
\ifboolfalse{proofended}{%
\proofend%
}%
}
\prooflabel{Beweis}
\newenvironment {beweis} {%
\begin{proof}%
}{%
\end{proof}%
}
\newenvironment {Beweis} {%
\begin{Proof}%
}{%
\end{Proof}%
}
%------------------------------------------------------------------------------
% Induction environments
%------------------------------------------------------------------------------
\newcommand \vind[2]{\textit{Beweis mittels vollständiger Induktion über $#1$:}\\}
\newcommand \vindende {\indende{vollständige}}
\newcommand \sind {\textit{Beweis durch strukturelle Induktion:\\}}
\newcommand \sindende {\indende{strukturelle}}
\newcommand{\indanf}[2]
{Induktionsanfang ($#1=#2$):}
\newcommand{\indanfs}
{Induktionsanfang:}
\newcommand{\indvor}
{Induktionsvoraussetzung:}
\newcommand{\indschritt}
{Induktionsschritt:}
\newcommand{\indende}[1]
{Nach dem Prinzip der #1n Induktion folgt die Behauptung.\proofend}
%------------------------------------------------------------------------------
% equivalence and set equality proofs
%------------------------------------------------------------------------------
\newcommand \hinsymb {\glqq$\mathbf{\Rightarrow}$\grqq}
\newcommand \ruecksymb {\glqq$\mathbf{\Leftarrow}$\grqq}
\newcommand \sethinsymb {\glqq$\mathbf{\subseteq}$\grqq}
\newcommand \setruecksymb {\glqq$\mathbf{\supseteq}$\grqq}
\newcommand \ssethinsymb {\glqq$\mathbf{\subset}$\grqq}
\newcommand \ssetruecksymb {\glqq$\mathbf{\supset}$\grqq}
\newcommand \hin {\hinsymb \\*[2pt]}
\newcommand \rueck {\ruecksymb \\*[2pt]}
\newcommand \sethin {\sethinsymb \\*[2pt]}
\newcommand \setrueck {\setruecksymb \\*[2pt]}
\newcommand \ssethin {\ssethinsymb \\*[2pt]}
\newcommand \ssetrueck {\ssetruecksymb \\*[2pt]}
\newenvironment{equivproof}{%
\begin{proof}%
\begin{equivproof**}%
}{%
\proofend%
\end{equivproof**}%
\end{proof}%
}
\newenvironment{equivproof*}{%
\begin{proof*}%
\begin{equivproof**}%
}{%
\proofend%
\end{equivproof**}%
\end{proof*}%
}
\newenvironment{equivproof**}{%
\renewcommand \hin {\item[\hinsymb]}%
\renewcommand \rueck {\item[\ruecksymb]}%
\begin{itemize}%
}{%
\end{itemize}%
}
\newenvironment{setequalproof}{%
\begin{proof}%
\begin{setequalproof**}%
}{%
\proofend%
\end{setequalproof**}%
\end{proof}%
}
\newenvironment{setequalproof*}{%
\begin{proof*}%
\begin{setequalproof**}%
}{%
\proofend%
\end{setequalproof**}%
\end{proof*}%
}
\newenvironment{setequalproof**}{%
\renewcommand \sethin {\item[\sethinsymb]}%
\renewcommand \setrueck {\item[\setruecksymb]}%
\begin{itemize}%
}{%
\end{itemize}%
}
% infer
\newcommand \dinfer[2] {\text{$\displaystyle\infer{#1}{#2}$}}
\makeatother
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