proposition: Lemma rowgD m1 m2 (A : 'M_(m1, n)) (B : 'M_(m2, n)) : rowg (A + B)%MS = (rowg A * rowg B)%g.
proof: Proof. apply/eqP; rewrite eq_sym eqEcard mulG_subG /= !rowgS. rewrite addsmxSl addsmxSr -(@leq_pmul2r #|rowg A :&: rowg B|) ?cardG_gt0 //=. by rewrite -mul_cardG -rowgI !card_rowg -!expnD mxrank_sum_cap. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime) mathcomp(ssralg poly finset fingroup morphism perm) mathcomp(automorphism quotient gproduct action finalg) mathcomp(zmodp commutator cyclic center pgroup gseries) mathcomp(nilpotent sylow maximal abelian matrix) mathcomp(mxalgebra mxrepresentation)