Section NaryDirect.
Context {I : finType} {P : pred I}.

Lemma directv_sum_unique {Us : I -> {vspace vT}} :
reflect (forall us vs,
(forall i, P i -> us i \in Us i) ->
(forall i, P i -> vs i \in Us i) ->
(\sum_(i | P i) us i == \sum_(i | P i) vs i)
= [forall (i | P i), us i == vs i])
(directv (\sum_(i | P i) Us i)).