Two new conjectures

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

A stronger conjecture:

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

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

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