\usepackage[ngerman]{babel}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{color}
\usepackage{enumerate}
\usepackage[framed,amsmath,thmmarks,hyperref]{ntheorem}
\usepackage{framed}
\usepackage{makeidx}
\usepackage{ntheorem}
\usepackage{stmaryrd}
\usepackage[bookmarks,bookmarksnumbered,pdfpagelayout=OneColumn,colorlinks]{hyperref}

% mathematische Operatoren
\DeclareMathOperator{\Abb}{Abb}
\DeclareMathOperator{\Aut}{Aut}
\DeclareMathOperator{\Autaff}{Aut_{aff}}
\DeclareMathOperator{\Autdist}{Aut_{dist}}
\DeclareMathOperator{\Bil}{Bil}
\DeclareMathOperator{\Char}{Char}
\DeclareMathOperator{\card}{card}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\End}{End}
\DeclareMathOperator{\ggT}{ggT}
\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\Grad}{Grad}
\DeclareMathOperator{\Hom}{Hom}
\DeclareMathOperator{\Homaff}{Hom_{aff}}
\DeclareMathOperator{\id}{id}
\DeclareMathOperator{\Imag}{Im}
\DeclareMathOperator{\JNF}{JNF}
\DeclareMathOperator{\Kern}{Kern}
\DeclareMathOperator{\Real}{Re}
\DeclareMathOperator{\rank}{rg}
\DeclareMathOperator{\Spec}{Spec}
\DeclareMathOperator{\Supp}{Supp}
\DeclareMathOperator{\SKP}{\langle\cdot,\cdot\rangle}

\definecolor{Red}{rgb}{1,0,0}


% Sätze
\theoremstyle{break}
\theoremseparator{:}
\theoremheaderfont{\sffamily\bfseries}
\theorembodyfont{}
\newframedtheorem{theo}{Satz}
\newframedtheorem{supptheo}{Hilfssatz}

\theoremstyle{nonumberbreak}
\newframedtheorem{corollary}{Korollar}
\newframedtheorem{lemma}{Lemma}

%Zeichen
\def\vk{\varkappa}
\def\vp{\varphi}

%allgemeines für Umgebungen
\renewcommand{\labelenumi}{(\arabic{enumi})}
\renewcommand{\labelenumii}{(\alph{enumii})}
\theoremstyle{nonumberplain}
\theoremseparator{:}

% Umgebungen mit passenden Einrückungen
\newlength{\applicationlength}
\settowidth{\applicationlength}{\sffamily\bfseries{}Anwendung: }
\theoremheaderfont{\hspace{-\applicationlength}\sffamily\bfseries}
\theorembodyfont{}
\theoremindent\applicationlength
\newtheorem{application}{Anwendung}

\newlength{\tasklength}
\settowidth{\tasklength}{\sffamily\bfseries{}Aufgabe: }
\theoremheaderfont{\hspace{-\tasklength}\sffamily\bfseries}
\theorembodyfont{}
\theoremindent\tasklength
\newtheorem{task}{Aufgabe}

\newlength{\commentlength}
\settowidth{\commentlength}{\sffamily\bfseries{}Bemerkung: }
\theoremheaderfont{\hspace{-\commentlength}\sffamily\bfseries}
\theorembodyfont{}
\theoremindent\commentlength
\newtheorem{comment}{Bemerkung}

\newlength{\examplelength}
\settowidth{\examplelength}{\sffamily\bfseries{}Beispiel: }
\theoremheaderfont{\hspace{-\examplelength}\sffamily\bfseries}
\theorembodyfont{}
\theoremindent\examplelength
\newtheorem{example}{Beispiel}

\newlength{\notelength}
\settowidth{\notelength}{\sffamily\bfseries{}Beachte: }
\theoremheaderfont{\hspace{-\notelength}\sffamily\bfseries}
\theorembodyfont{}
\theoremindent\notelength
\newtheorem{note}{Beachte}

\newlength{\thesislength}
\settowidth{\thesislength}{\sffamily\bfseries{}Behauptung: }
\theoremheaderfont{\hspace{-\thesislength}\sffamily\bfseries}
\theorembodyfont{}
\theoremindent\thesislength
\newtheorem{thesis}{Behauptung}

\newlength{\prooflength}
\settowidth{\prooflength}{\sffamily\bfseries{}Beweis: }
\theoremheaderfont{\hspace{-\prooflength}\sffamily\bfseries}
\theorembodyfont{}
\theoremindent\prooflength
\theoremsymbol{\ensuremath{_\blacksquare}}
\newtheorem{proof}{Beweis}

\theoremsymbol{}

\newenvironment{definition}{\begin{define}\renewcommand{\labelenumi}{(\alph{enumi})}}{\renewcommand{\labelenumi}{(\arabic{enumi})}\end{define}}
\newlength{\definitionlength}
\settowidth{\definitionlength}{\sffamily\bfseries{}Definition: }
\theoremheaderfont{\hspace{-\definitionlength}\sffamily\bfseries}
\theorembodyfont{}
\theoremindent\definitionlength
\newtheorem{define}{Definition}

\newlength{\remindlength}
\settowidth{\remindlength}{\sffamily\bfseries{}Erinnere: }
\theoremheaderfont{\hspace{-\remindlength}\sffamily\bfseries}
\theorembodyfont{}
\theoremindent\remindlength
\newtheorem{remind}{Erinnere}

\newlength{\conclusionlength}
\settowidth{\conclusionlength}{\sffamily\bfseries{}Folgerung: }
\theoremheaderfont{\hspace{-\conclusionlength}\sffamily\bfseries}
\theorembodyfont{}
\theoremindent\conclusionlength
\newtheorem{conclusion}{Folgerung}

\newlength{\methodlength}
\settowidth{\methodlength}{\sffamily\bfseries{}Methode: }
\theoremheaderfont{\hspace{-\methodlength}\sffamily\bfseries}
\theorembodyfont{}
\theoremindent\methodlength
\newtheorem{method}{Methode}

\newlength{\problemlength}
\settowidth{\problemlength}{\sffamily\bfseries{}Problem: }
\theoremheaderfont{\hspace{-\problemlength}\sffamily\bfseries}
\theorembodyfont{}
\theoremindent\problemlength
\newtheorem{problem}{Problem}

\newlength{\propositionlength}
\settowidth{\propositionlength}{\sffamily\bfseries{}Proposition: }
\theoremheaderfont{\hspace{-\propositionlength}\sffamily\bfseries}
\theorembodyfont{}
\theoremindent\propositionlength
\newtheorem{proposition}{Proposition}

\newlength{\strategielength}
\settowidth{\strategielength}{\sffamily\bfseries{}Strategie: }
\theoremheaderfont{\hspace{-\strategielength}\sffamily\bfseries}
\theorembodyfont{}
\theoremindent\strategielength
\newtheorem{strategie}{Strategie}

\newlength{\preremlength}
\settowidth{\preremlength}{\sffamily\bfseries{}Vorbemerkung: }
\theoremheaderfont{\hspace{-\preremlength}\sffamily\bfseries}
\theorembodyfont{}
\theoremindent\preremlength
\newtheorem{prerem}{Vorbemerkung}

\newlength{\cautionlength}
\settowidth{\cautionlength}{\sffamily\bfseries{}Vorsicht: }
\theoremheaderfont{\hspace{-\cautionlength}\sffamily\bfseries}
\theorembodyfont{}
\theoremindent\cautionlength
\newtheorem{caution}{Vorsicht}

\newlength{\preplength}
\settowidth{\preplength}{\sffamily\bfseries{}Vorbereitung: }
\theoremheaderfont{\hspace{-\preplength}\sffamily\bfseries}
\theorembodyfont{}
\theoremindent\preplength
\newtheorem{prep}{Vorbereitung}

\newlength{\prepworklength}
\settowidth{\prepworklength}{\sffamily\bfseries{}Vorarbeit: }
\theoremheaderfont{\hspace{-\prepworklength}\sffamily\bfseries}
\theorembodyfont{}
\theoremindent\prepworklength
\newtheorem{prepwork}{Vorarbeit}

\newlength{\ziellength}
\settowidth{\ziellength}{\sffamily\bfseries{}Ziel: }
\theoremheaderfont{\hspace{-\ziellength}\sffamily\bfseries}
\theorembodyfont{}
\theoremindent\ziellength
\newtheorem{ziel}{Ziel}

\newlength{\zwecklength}
\settowidth{\zwecklength}{\sffamily\bfseries{}Zweck: }
\theoremheaderfont{\hspace{-\zwecklength}\sffamily\bfseries}
\theorembodyfont{}
\theoremindent\zwecklength
\newtheorem{zweck}{Zweck}
