Distributivity of composition over join of reloids

In the last version of Reloids and Funcoids online article I proved true the following conjecture:

Theorem
If $latex f$, $latex g$, $latex h$ are reloids then

• $latex f\circ (g\cup^{\mathsf{RLD}} h) = f\circ g \cup^{\mathsf{RLD}} f\circ h$;
• $latex (g\cup^{\mathsf{RLD}} h) \circ f = g\circ f \cup^{\mathsf{RLD}} h\circ f$.