Section GeneratedGroup.
Variable gT : finGroupType.
Implicit Types x y z : gT.
Implicit Types A B C D : {set gT}.
Implicit Types G H K : {group gT}.

Lemma bigprodGE I r (P : pred I) (F : I -> {group gT}) :
(\prod_(i <- r | P i) F i)%G :=: << \bigcup_(i <- r | P i) F i >>.