Completion of a join of reloids

I proved true the following conjecture:

Theorem \mathrm{Compl} \left( \bigcup^{\mathsf{RLD}} R \right) = \bigcup ^{\mathsf{RLD}} \langle \mathrm{Compl} \rangle R for every set R of reloids.

The following conjecture remains open:

Conjecture \mathrm{Compl}\,f \cap^{\mathsf{RLD}} \mathrm{Compl}\,g =\mathrm{Compl} (f \cap^{\mathsf{RLD}} g) for every reloids f and g.

See here for definitions and proofs.

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