A new theorem about subatimic product

I recently discovered what I call subatomic product of funcoids.

Today I proved a simple theorem about subatomic product:

Theorem $latex \prod^{\left( A \right)}_{i \in n} \left( g_i \circ f_i \right) = \prod^{\left( A \right)} g \circ \prod^{\left( A \right)} f$ for indexed (by an index set $latex n$) families $latex f$ and $latex g$ of funcoids such that $latex \forall i \in n : \mathrm{Dst}\,f_i =\mathrm{Src}\,g_i$.