proposition: Lemma mxrank_tr m n (A : 'M_(m, n)) : \rank A^T = \rank A.
proof: Proof. apply/eqP; rewrite eqn_leq -{3}[A]trmxK -{1}(mulmx_base A) -{1}(mulmx_base A^T). by rewrite !trmx_mul !mulmx_max_rank. 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)