Section RowGroup.
Variable n : nat.
Local Notation rVn := 'rV[F]_n.
Definition rowg m (A : 'M[F]_(m, n)) : {set rVn} := [set u | u <= A]%MS.
Canonical rowg_group m A := Group (@rowg_group_set m A).

Lemma bigcprod_rowg m I r (P : pred I) (A : I -> 'M[F]_n) (B : 'M[F]_(m, n)) :
(\sum_(i <- r | P i) A i :=: B)%MS ->
\big[cprod/1%g]_(i <- r | P i) rowg (A i) = rowg B.