# Restricting a reloid to a trivial atomic filter object

I proved the following (not very hard) theorem:

Theorem $f|^{\mathsf{RLD}}_{\{ \alpha \}} = \{ \alpha \} \times^{\mathsf{RLD}} \mathrm{im} \left( f|^{\mathsf{RLD}}_{\{ \alpha \}} \right)$ for every reloid $f$ and $\alpha \in \mho$.