\documentclass[a4paper,10pt]{article}
\usepackage{amssymb}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Author: Thomas Braun
% begin: Sat 8 april 2006
% last edit: Mo 9 april 2007
% License: GPLv2 or later
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\iffalse
\newcommand{\begin{neededpkgs}}[2][]{}
\newcommand{\pkgs}[2][]{}
\fi

\input{definitions}

\begin{document}

\mathcommand{\bowtie}
\pkgs{amssymb}\mathcommand{\Join}
\mathcommand{\propto}
\begin{neededpkgs}{amssymb}
\mathcommand{\varpropto}
\mathcommand{\multimap}
\mathcommand{\pitchfork}
\mathcommand{\therefore}
\mathcommand{\because}
\end{neededpkgs}

\mathcommand{=}
\mathcommand{\neq}
\mathcommand{\equiv}
\begin{neededpkgs}{amssymb}
\end{neededpkgs}
\mathcommand{\approx}
\mathcommand{\sim}
\begin{neededpkgs}{amssymb}
\end{neededpkgs}
\mathcommand{\simeq}
\pkgs{amssymb}\mathcommand{\backsimeq}
\pkgs{amssymb}\mathcommand{\approxeq}
\mathcommand{\cong}
\pkgs{amssymb}\mathcommand{\ncong}

\mathcommand{\smile}
\mathcommand{\frown}
\mathcommand{\asymp}
\begin{neededpkgs}{amssymb}
\mathcommand{\smallfrown}
\mathcommand{\smallsmile}
\mathcommand{\between}
\end{neededpkgs}
\mathcommand{\prec}
\mathcommand{\succ}
\pkgs{amssymb}\mathcommand{\nprec}
\pkgs{amssymb}\mathcommand{\nsucc}
\mathcommand{\preceq}
\mathcommand{\succeq}
\begin{neededpkgs}{amssymb}
\mathcommand{\npreceq}
\mathcommand{\nsucceq}

\mathcommand{\preccurlyeq}
\mathcommand{\succcurlyeq}
\mathcommand{\curlyeqprec}
\mathcommand{\curlyeqsucc}
\mathcommand{\precsim}
\mathcommand{\succsim}
\mathcommand{\precnsim}
\mathcommand{\succnsim}
\mathcommand{\precapprox}
\mathcommand{\succapprox}
\mathcommand{\precnapprox}
\mathcommand{\succnapprox}

\end{neededpkgs}
\mathcommand{\perp}
\mathcommand{\vdash}
\mathcommand{\dashv}
\begin{neededpkgs}{amssymb}
\mathcommand{\nvdash}
\mathcommand{\Vdash}
\mathcommand{\Vvdash}
\end{neededpkgs}
\mathcommand{\models}
\begin{neededpkgs}{amssymb}
\mathcommand{\vDash}
\mathcommand{\nvDash}
\mathcommand{\nVDash}
\end{neededpkgs}

\mathcommand{\mid}
\pkgs{amssymb}\mathcommand{\nmid}
\mathcommand{\parallel}
\begin{neededpkgs}{amssymb}
\mathcommand{\nparallel}
\mathcommand{\shortmid}
\mathcommand{\nshortmid}
\mathcommand{\shortparallel}
\mathcommand{\nshortparallel}
\end{neededpkgs}

\mathcommand{<}
\mathcommand{>}
\begin{neededpkgs}{amssymb}
\mathcommand{\nless}
\mathcommand{\ngtr}
\mathcommand{\lessdot}
\mathcommand{\gtrdot}
\end{neededpkgs}

\mathcommand{\ll}
\mathcommand{\gg}
\pkgs{amssymb}\mathcommand{\lll}
\pkgs{amssymb}\mathcommand{\ggg}

\mathcommand{\leq}
\mathcommand{\geq}
\begin{neededpkgs}{amssymb}
\mathcommand{\lneq}
\mathcommand{\gneq}
\mathcommand{\nleq}
\mathcommand{\ngeq}
\mathcommand{\leqq}
\mathcommand{\geqq}
\mathcommand{\lneqq}
\mathcommand{\gneqq}
\mathcommand{\lvertneqq}
\mathcommand{\gvertneqq}
\mathcommand{\nleqq}
\mathcommand{\ngeqq}

\mathcommand{\leqslant}
\mathcommand{\geqslant}
\mathcommand{\nleqslant}
\mathcommand{\ngeqslant}
\mathcommand{\eqslantless}
\mathcommand{\eqslantgtr}

\mathcommand{\lessgtr}
\mathcommand{\gtrless}
\mathcommand{\lesseqgtr}
\mathcommand{\gtreqless}
\mathcommand{\lesseqqgtr}
\mathcommand{\gtreqqless}

\mathcommand{\lesssim}
\mathcommand{\gtrsim}
\mathcommand{\lnsim}
\mathcommand{\gnsim}
\mathcommand{\lessapprox}
\mathcommand{\gtrapprox}
\mathcommand{\lnapprox}
\mathcommand{\gnapprox}


\mathcommand{\vartriangleleft}
\mathcommand{\vartriangleright}
\mathcommand{\ntriangleleft}
\mathcommand{\ntriangleright}
\mathcommand{\trianglelefteq}
\mathcommand{\trianglerighteq}
\mathcommand{\ntrianglelefteq}
\mathcommand{\ntrianglerighteq}
\mathcommand{\blacktriangleleft}
\mathcommand{\blacktriangleright}
\end{neededpkgs}

\mathcommand{\subset}
\mathcommand{\supset}
\mathcommand{\subseteq}
\mathcommand{\supseteq}
\begin{neededpkgs}{amssymb}
\mathcommand{\subsetneq}
\mathcommand{\supsetneq}
\mathcommand{\varsubsetneq}
\mathcommand{\varsupsetneq}
\mathcommand{\nsubseteq}
\mathcommand{\nsupseteq}
\mathcommand{\subseteqq}
\mathcommand{\supseteqq}
\mathcommand{\subsetneqq}
\mathcommand{\supsetneqq}
\mathcommand{\nsubseteqq}
\mathcommand{\nsupseteqq}
\mathcommand{\backepsilon}

\mathcommand{\Subset}
\mathcommand{\Supset}
\mathcommand{\sqsubset}
\mathcommand{\sqsupset}
\end{neededpkgs}
\mathcommand{\sqsubseteq}
\mathcommand{\sqsupseteq}

\end{document}