proposition: Lemma col_mx_eq0 (m1 m2 n : nat) (A1 : 'M_(m1, n)) (A2 : 'M_(m2, n)): (col_mx A1 A2 == 0) = (A1 == 0) && (A2 == 0).
proof: Proof. by rewrite -![_ == 0](inj_eq trmx_inj) !trmx0 tr_col_mx row_mx_eq0. 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 countalg finalg zmodp)