proposition: Lemma mxdirect_addsP (A : 'M_(m1, n)) (B : 'M_(m2, n)) : reflect (A :&: B = 0)%MS (mxdirect (A + B)).
proof: Proof. by rewrite mxdirect_addsE !mxdirect_trivial; apply: eqP. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype finfun bigop finset fingroup perm order) mathcomp(div prime binomial ssralg finalg zmodp matrix)