Two conjectures proved

In this online article I’ve proved:

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

and its easy consequence:

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

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