New conjecture:

Conjecture $\mathrm{up} (f \sqcap^{\mathsf{FCD}} g) \subseteq \{ F \sqcap G \mid F \in \mathrm{up}\, f, G \in \mathrm{up}\, g \}$ for all funcoids $f$, $g$ (with corresponding sources and destinations).

Looks trivial? But how to (dis)prove it?