(* Matrix multiplication using bigops. *)
Definition mulmx {m n p} (A : 'M_(m, n)) (B : 'M_(n, p)) : 'M[R]_(m, p) :=
\matrix[mulmx_key]_(i, k) \sum_j (A i j * B j k).
Local Notation "A *m B" := (mulmx A B) : ring_scope.

Lemma mulmxDl m n p (A1 A2 : 'M_(m, n)) (B : 'M_(n, p)) :
(A1 + A2) *m B = A1 *m B + A2 *m B.