I’ve proved one more conjecture

I’ve proved yet one conjecture.

The proof is presented in this online article.

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}.

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