\newcommand{\hb}{{\rightarrow}}
\newcommand{\nhb}{{\not \rightarrow}}
\newcommand{\tc}{{\hookrightarrow}}
\newcommand{\ntc}{{\not \hookrightarrow}}
\newcommand{\ind}{{\mid}}
\newcommand{\pc}{{\stackrel{p}{\tc}}}
\newcommand{\npc}{{\not\stackrel{p}{\tc}}}
\newcommand{\pind}{{{\ind_p}}}
\newcommand{\implies}{{\Rightarrow}}
\newcommand{\revImplies}{{\Leftarrow}}
\newtheorem{definition}{Definition}
