proposition: Lemma mul_pid_mx_copid m n r : r <= n -> pid_mx r *m copid_mx r = 0 :> 'M_(m, n).
proof: Proof. by move=> le_r_n; rewrite mulmxBr mulmx1 pid_mx_id ?subrr. 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)