# A new function which is a counter-example to a conjecture found

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

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

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

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