\newcommand{\nb}[1]{{\color{blue} NB: #1}}

\newtheorem{theorem}{Theorem}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{lemma}[theorem]{Lemma}


\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}


\newcommand{\wit}[2]{\mathit{wit}^{#1}_{#2}}
\newcommand{\Wit}[2]{\mathit{Wit}^{#1}_{#2}}
\newcommand{\dfn}{:=}
\newcommand{\seqar}{\rightarrow}
\newcommand{\proves}{\vdash}


\newcommand{\safe}{\sigma}
\newcommand{\normal}{\nu}

\newcommand{\pv}{\mathit{PV}}
\newcommand{\pvbci}[1]{\pv^{#1}_{\mathrm{BC}}}
\newcommand{\mubci}[1]{\mu\mathrm{BC}^{#1}}
\newcommand{\bc}{\mathrm{BC}}

\newcommand{\fphi}[1]{\Box_{#1}}
	\newcommand{\ph}{\mathbf{PH}}
	\newcommand{\pspace}{\mathbf{PSPACE}}
	\newcommand{\fpspace}{\mathbf{FPSPACE}}
	\newcommand{\ptime}{\mathbf{P}}
	\newcommand{\fptime}{\mathbf{FP}}
	\newcommand{\nc}{\mathbf{NC}}
	\newcommand{\ac}{\mathbf{AC}}
	\newcommand{\exptime}{\mathbf{EXP}}
	

\newcommand{\cnot}{\neg}
\newcommand{\cimp}{\supset}
\newcommand{\cor}{\vee}
\newcommand{\cand}{\wedge}
\newcommand{\ciff}{\equiv}