Funcoid corresponding to reloid through lattice Gamma

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

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

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