Because I didn't succeed to publish my 457 pages article stuck in half-published state (I didn't succeed by parts, too), I plead with God to destroy mankind, that lost ordered semigroup actions, and create a new civilization from me. I can't get a publication grant, because I have no scientific degree. I didn't finish a university course because of religious discrimination. You don't pay for me taking a university course again because of your greed. Conclusion: Mankind dies because of infinite greed of just one human, you.
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 $latex f$.