After removing an erroneous theorem I posed two new open problems to take its place:
Conjecture If $latex f$ is a complete funcoid and $latex R$ is a set of funcoids then $latex f \circ \bigcup {\nobreak}^{\mathsf{FCD}} R = \bigcup {\nobreak}^{\mathsf{FCD}} \langle f \circ \rangle R$.
Conjecture If $latex f$ is a complete reloid and $latex R$ is a set of reloids then $latex f \circ \bigcup {\nobreak}^{\mathsf{RLD}} R = \bigcup {\nobreak}^{\mathsf{RLD}} \langle f \circ \rangle R$.
These conjectures may be weakened:
Conjecture If $latex f$ is a discrete funcoid and $latex R$ is a set of funcoids then $latex f \circ \bigcup {\nobreak}^{\mathsf{FCD}} R = \bigcup {\nobreak}^{\mathsf{FCD}} \langle f \circ \rangle R$.
Conjecture If $latex f$ is a discrete reloid and $latex R$ is a set of reloids then $latex f \circ \bigcup {\nobreak}^{\mathsf{RLD}} R = \bigcup {\nobreak}^{\mathsf{RLD}} \langle f \circ \rangle R$.