proposition: Lemma lt_eqmx m1 m2 m3 n (A : 'M_(m1, n)) (B : 'M_(m2, n)) : (A :=: B)%MS -> forall C : 'M_(m3, n), (((A < C) = (B < C))%MS * ((C < A) = (C < B))%MS)%type.
proof: Proof. by move=> eqAB C; rewrite /ltmx !eqAB. 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)