proposition: Lemma mul_diag_mx_pid m n p r s : r <= p -> diag_mx_seq m p s *m @pid_mx R p n r = diag_mx_seq m n (take r s).
proof: Proof. move=> le_r_p; rewrite -[_ *m _]trmxK trmx_mul_rev tr_pid_mx tr_diag_mx_seq. by rewrite mul_pid_mx_diag // tr_diag_mx_seq. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq path) mathcomp(ssralg fintype perm poly mxpoly finfun tuple) mathcomp(matrix bigop zmodp polydiv) ssrcomplements dvdring