I’ve published in my book’s preprint a theorem (currently numbered 6.100) which solves a former conjecture.

**Theorem** $latex g \circ \left( \bigsqcup R \right) = \bigsqcup \left\{ g \circ f \,|\, g \in R \right\} = \bigsqcup \langle g \circ \rangle R$ if $latex g$ is a complete funcoid.

My shame, I have earlier overlooked an almost obvious proof.