Example

The function $u \rightarrow d(u)$ is moderately increasing (§7, no. 5, Cor. 1 of Th. 3); for any norm $\| \|$ on $\mathbf{R}\otimes X(T)$, the function $u \rightarrow \|\lambda (u)\|$ is moderately increasing. For any Casimir element $\Gamma$, the function $u \rightarrow \widetilde{\Gamma}(u)$ is moderately increasing; more generally: