Theorem For every funcoid $f$ and filters $\mathcal{X}\in\mathfrak{F}(\mathrm{Src}\,f)$, $\mathcal{Y}\in\mathfrak{F}(\mathrm{Dst}\,f)$:
1. $\mathcal{X} \mathrel{[(\mathsf{FCD}) f]} \mathcal{Y} \Leftrightarrow \forall F \in \mathrm{up}^{\Gamma (\mathrm{Src}\, f ; \mathrm{Dst}\, f)} f : \mathcal{X} \mathrel{[F]} \mathcal{Y}$;
2. $\langle (\mathsf{FCD}) f \rangle \mathcal{X} = \bigsqcap_{F \in \mathrm{up}^{\Gamma (\mathrm{Src}\, f ; \mathrm{Dst}\, f)} f} \langle F \rangle \mathcal{X}$.