Local Notation "'Zm" := (scale_action _ _) (at level 8) : action_scope.
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.

Lemma bigdprod_rowg m (I : finType) (P : pred I) A (B : 'M[F]_(m, n)) :
let S := (\sum_(i | P i) A i)%MS in (S :=: B)%MS -> mxdirect S ->
\big[dprod/1%g]_(i | P i) rowg (A i) = rowg B.