I’ve proved this my conjecture:

$latex g \circ f = \bigsqcap \left\{ G \circ F \,|\, F \in \mathrm{up}\, f, G \in \mathrm{up}\, g \right\}$ for every composable funcoids $latex f$ and $latex g$.

See my book (in the current draft the theorem 6.65) for a proof.