A different definition of product of funcoids

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.

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