I’ve proved one more conjecture

I’ve proved yet one conjecture.

The proof is presented in this online article.

Theorem For every funcoid $latex f$ and filters $latex \mathcal{X}\in\mathfrak{F}(\mathrm{Src}\,f)$, $latex \mathcal{Y}\in\mathfrak{F}(\mathrm{Dst}\,f)$:

1. $latex \mathcal{X} \mathrel{[(\mathsf{FCD}) f]} \mathcal{Y}
   \Leftrightarrow \forall F \in \mathrm{up}^{\Gamma (\mathrm{Src}\, f ; \mathrm{Dst}\,
   f)} f : \mathcal{X} \mathrel{[F]} \mathcal{Y}$;

2. $latex \langle (\mathsf{FCD}) f \rangle \mathcal{X} = \bigsqcap_{F
   \in \mathrm{up}^{\Gamma (\mathrm{Src}\, f ; \mathrm{Dst}\, f)} f} \langle F \rangle
   \mathcal{X}$.