Explain why the companion \\(\widehat{\mathrm{id}}\\) of \\(\mathrm{id}:\mathcal{P}\to\mathcal{P}\\) really has the formula given in Eq. \eqref{eq1}.

\begin{equation}\label{eq1}\tag{4.25}U_{\mathcal{X}}(x,y):=\mathcal{X}(x,y).\end{equation}