Refer to this draft for more details.

Conjecture Let S be a set of \mathbf{Rel}-morphisms. If \forall X, Y \in S: \operatorname{up} (X \sqcap^{\mathsf{FCD}} Y)
\subseteq S then \operatorname{up} (X_0 \sqcap^{\mathsf{FCD}} \ldots
\sqcap^{\mathsf{FCD}} X_n) \subseteq S for X_i \in S.

Trying to prove the above conjecture, first prove the following lemma:

Lemma For every funcoid f and filter Failed to parse (unknown function\mathscr): \mathcal{X} \in \mathscr{F} (\operatorname{Src} f)

\operatorname{up} \langle f \rangle \mathcal{X} = \bigcup_{F \in \operatorname{up} f}
   \operatorname{up} \langle F \rangle \mathcal{X} = \left\{ K \in \operatorname{up} \langle F
   \rangle \mathcal{X} \mid F \in \operatorname{up} f \right\}.

Ad blocker interference detected!

Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.