Two propositions and a conjecture

I added to Funcoids and Reloids article the following two new propositions and a conjecture:

Proposition $latex (\mathsf{FCD}) (f\cap^{\mathsf{RLD}} ( \mathcal{A}\times^{\mathsf{RLD}} \mathcal{B})) = (\mathsf{FCD}) f \cap^{\mathsf{FCD}} (\mathcal{A}\times^{\mathsf{FCD}} \mathcal{B})$ for every reloid $latex f$ and filter objects $latex \mathcal{A}$ and $latex \mathcal{B}$.

Proposition $latex ( \mathsf{RLD})_{\mathrm{in}} (f \cap^{\mathsf{FCD}} ( \mathcal{A} \times^{\mathsf{FCD}} \mathcal{B})) = (( \mathsf{RLD})_{\mathrm{in}} f) \cap^{\mathsf{RLD}} ( \mathcal{A} \times^{\mathsf{RLD}} \mathcal{B})$ for every funcoid $latex f$ and filter objects $latex \mathcal{A}$ and $latex \mathcal{B}$.

Question $latex ( \mathsf{RLD})_{\mathrm{out}} (f \cap^{\mathsf{FCD}} ( \mathcal{A} \times^{\mathsf{FCD}} \mathcal{B})) = (( \mathsf{RLD})_{\mathrm{out}} f) \cap^{\mathsf{RLD}} ( \mathcal{A} \times^{\mathsf{RLD}} \mathcal{B})$ for every funcoid $latex f$ and filter objects $latex \mathcal{A}$ and $latex \mathcal{B}$?