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I’ve proved this my conjecture:

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

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

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