proposition: Lemma ltmx_sub_trans m1 m2 m3 n (A : 'M_(m1, n)) (B : 'M_(m2, n)) (C : 'M_(m3, n)) : (A < B)%MS -> (B <= C)%MS -> (A < C)%MS.
proof: Proof. case/andP=> sAB ltAB sBC; rewrite ltmxE (submx_trans sAB) //. by apply: contra ltAB; apply: submx_trans. 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)