Arguments cent_mxP {m n B R}.

(* Specifications: *)
Lemma scalar_mx_cent m n a (R : 'A_(m, n)) : (a%:M \in 'C(R))%MS.
Arguments center_mxP {m n A R}.
Lemma mxring_id_uniq m n (R : 'A_(m, n)) e1 e2 :
mxring_id R e1 -> mxring_id R e2 -> e1 = e2.
Lemma cent_mx_ideal m n (R : 'A_(m, n)) : left_mx_ideal 'C(R)%MS 'C(R)%MS.
Lemma cent_mx_ring m n (R : 'A_(m, n)) : n > 0 -> mxring 'C(R)%MS.
Lemma mxdirect_adds_center m1 m2 n (R1 : 'A_(m1, n)) (R2 : 'A_(m2, n)) :
mx_ideal (R1 + R2)%MS R1 -> mx_ideal (R1 + R2)%MS R2 ->
mxdirect (R1 + R2) ->
('Z((R1 + R2)%MS) :=: 'Z(R1) + 'Z(R2))%MS.
Lemma mxdirect_sums_center (I : finType) m n (R : 'A_(m, n)) R_ :
(\sum_i R_ i :=: R)%MS -> mxdirect (\sum_i R_ i) ->
(forall i : I, mx_ideal R (R_ i)) ->
('Z(R) :=: \sum_i 'Z(R_ i))%MS.