In this online article I’ve proved:

**Theorem** $latex \mathrm{dom}\, (\mathsf{RLD})_{\mathrm{in}} f = \mathrm{dom}\, f$ and $latex \mathrm{im}\, (\mathsf{RLD})_{\mathrm{in}} f = \mathrm{im}\, f$ for every funcoid $latex f$.

and its easy consequence:

**Proposition** $latex \mathrm{dom}\, (\mathsf{RLD})_{\Gamma} f = \mathrm{dom}\, f$ and $latex \mathrm{im}\, (\mathsf{RLD})_{\Gamma} f = \mathrm{im}\, f$ for every funcoid $latex f$.