Local Notation MV := 'M[V]_(m, n).

(* Specifications: *)
Lemma map_mx0 : 0^f = 0 :> 'M_(m, n).
Lemma map_mxN A : (- A)^f = - A^f.
Lemma map_mxD A B : (A + B)^f = A^f + B^f.
Lemma map_mx_sub A B : (A - B)^f = A^f - B^f.