Definition $a \mathrel{\left[ \prod^{(A 2)} f \right]} b \Leftrightarrow \exists M \in \mathrm{fin} \forall i \in (\mathrm{dom}\, f) \setminus M : \Pr^{\mathsf{RLD}}_i a \mathrel{[f_i]} \Pr^{\mathsf{RLD}}_i b$ for an indexed family $f$ of funcoids and atomic reloids $a$ and $b$ of suitable form. Here $M \in \mathrm{fin}$ means that $M$ is a finite set.
Conjecture Funcoid $\prod^{(A 2)} f$ exists.