Two new conjectures

Conjecture If $latex a\times^{\mathsf{RLD}} b\subseteq(\mathsf{RLD})_{\mathrm{in}} f$ then $latex a\times^{\mathsf{FCD}} b\subseteq f$ for every funcoid $latex f$ and atomic f.o. $latex a$ and $latex b$ on the source and destination of $latex f$ correspondingly.

A stronger conjecture:

Conjecture If $latex \mathcal{A}\times^{\mathsf{RLD}} \mathcal{B}\subseteq(\mathsf{RLD})_{\mathrm{in}} f$ then $latex \mathcal{A}\times^{\mathsf{FCD}} \mathcal{B}\subseteq f$ for every funcoid $latex f$ and $latex \mathcal{A}\in\mathfrak{F}(\mathrm{Src}\,f)$, $latex \mathcal{B}\in\mathfrak{F}(\mathrm{Dst}\,f)$.

Solution of these conjectures (specifically the first one) may help to prove other conjectures.