Section SquareBlockMatrixRing.
Context {R : ringType} {p : nat} {p_ : 'I_p -> nat}.
Notation sp := (\sum_i p_ i)%N.
Implicit Type (s : 'I_sp).

Lemma mul_mxdiag_mxcol m
(D_ : forall i, 'M[R]_(p_ i)) (C_ : forall i, 'M[R]_(p_ i, m)):
\mxdiag_i D_ i *m \mxcol_i C_ i = \mxcol_i (D_ i *m C_ i).