Section OneProd.
Variables G H K : {group gT}.
Hypothesis sGD : G \subset D.
End OneProd.
Implicit Type G : {group gT}.

Lemma injm_bigdprod I r (P : pred I) (H : I -> {group gT}) G :
G \subset D -> 'injm f -> \big[dprod/1]_(i <- r | P i) H i = G ->
\big[dprod/1]_(i <- r | P i) f @* H i = f @* G.