Section Injm.
Variables (rT : finGroupType) (D : {group gT}) (f : {morphism D >-> rT}).
Hypothesis injf : 'injm f.

Lemma center_bigcprod I r P (F : I -> {set gT}) G :
\big[cprod/1]_(i <- r | P i) F i = G ->
\big[cprod/1]_(i <- r | P i) 'Z(F i) = 'Z(G).