Canonical cprod_abelaw := Monoid.ComLaw cprodC.

Lemma bigcprodEY I r (P : pred I) (H : I -> {group gT}) G :
abelian G -> (forall i, P i -> H i \subset G) ->
\big[cprod/1]_(i <- r | P i) H i = (\prod_(i <- r | P i) H i)%G.