For this conjecture there was found a counter-example, see this online article.

The counter-example states that $latex (\mathsf{RLD})_{\Gamma} f \sqsupset (\mathsf{RLD})_{\mathrm{in}} f \sqsupset (\mathsf{RLD})_{\mathrm{out}} f$ for funcoid $latex f=(=)|_{\mathbb{R}}$.

This way I discovered a new function $latex (\mathsf{RLD})_{\Gamma}$ defined by the formula $latex (\mathsf{RLD})_{\Gamma} f = \bigsqcap^{\mathsf{RLD}} \mathrm{up}^{\Gamma (\mathrm{Src}\,f ; \mathrm{Dst}\,f)} f$.

While $latex (\mathsf{RLD})_{\mathrm{in}} f$ and $latex (\mathsf{RLD})_{\mathrm{out}} f$ have many cryptomorphisms (that is different but equivalent definitions) and lots of useful usages, all is known about $latex (\mathsf{RLD})_{\Gamma} f$ is its definition and the formula $latex (\mathsf{RLD})_{\Gamma} f \sqsupset (\mathsf{RLD})_{\mathrm{in}} f$. It is unclear whether $latex (\mathsf{RLD})_{\Gamma}$ is useful for anything.

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