proposition: Lemma mx_normZ (l : K) (x : 'M[K]_(m.+1, n.+1)) : `| l *: x | = `| l | * `| x |.
proof: Proof. rewrite {1 3}/normr /= !mx_normE (eq_bigr (fun i => (`|l| * `|x i.1 i.2|)%:nng)); last first. by move=> i _; rewrite mxE //=; apply/eqP; rewrite -num_eq /= normrM. elim/big_ind2 : _ => // [|a b c d bE dE]; first by rewrite mulr0. by rewrite !num_max bE dE maxr_pMr. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrint ssrnum finmap matrix) mathcomp(rat interval zmodp vector fieldext falgebra) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality set_interval Rstruct) ereal reals signed topology prodnormedzmodule