Section BlockMatrixRing.
Context {R : ringType} {p q : nat} {p_ : 'I_p -> nat} {q_ : 'I_q -> nat}.
Notation sp := (\sum_i p_ i)%N.
Notation sq := (\sum_i q_ i)%N.

Lemma mul_mxcol_mxrow m
(C_ : forall i, 'M[R]_(p_ i, m)) (R_ : forall j, 'M[R]_(m, q_ j)) :
\mxcol_i C_ i*m \mxrow_j R_ j  = \mxblock_(i, j) (C_ i *m R_ j).