$`\require{color} %\newcommand{\Imp}{\Rightarrow} % --- \newcommand{\In}{ \text{ in }} %\newcommand{\cat}[1]{\mathcal{#1} } %\newcommand{\id}{\mathrm{id} } %\newcommand{\Iff}{\Leftrightarrow} \newcommand{\mrm}[1]{ \mathrm{#1} } %\newcomman…