proposition: Lemma ltmxErank m1 m2 n (A : 'M_(m1, n)) (B : 'M_(m2, n)) : (A < B)%MS = (A <= B)%MS && (\rank A < \rank B).
proof: Proof. by apply: andb_id2l => sAB; rewrite (ltn_leqif (mxrank_leqif_sup sAB)). 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)