\newcommand{\fixpointsOf}{\textbf{\textit{fix}}}
\newcommand{\LL}{\mathcal{L}}
\newcommand{\lte}{\preceq}
\newcommand{\lteSub}[1]{\lteNoLink_{#1}}
\newcommand{\image}[1]{[#1]}
\newcommand{\define}{\coloneqq}
\newcommand{\union}{\cup}
\newcommand{\intersect}{\cap}
\newcommand{\glb}{\bigwedge}
\newcommand{\lub}{\bigvee}
\newcommand{\glbBinary}{\land}
\newcommand{\lubBinary}{\lor}
\newcommand{\powerset}{\wp}
\newcommand{\powersetO}{\wp^o}
\newcommand{\upclosure}{\uparrow}
\newcommand{\downclosure}{\downarrow}
\newcommand{\partialApp}{\cdot}
\newcommand{\lfp}{\textbf{lfp}}
\newcommand{\latticeinterval}[2]{[#1, #2]}

\newcommand{\Sdet}{S}
\newcommand{\Sdetbeta}{S^{\beta}}