proposition: Lemma prod_sympXY d (la : 'P_d) : 'hp[la](XY) = 'hp[la](X) * 'hp[la](Y).
proof: Proof. rewrite /prod_symp /prod_gen /= !rmorph_prod /=. rewrite -big_split /=; apply eq_bigr => i _. by rewrite [LHS]sympXY. Qed.
imports: HB(structures) mathcomp(all_ssreflect) mathcomp(ssrint rat ssralg ssrnum algC matrix vector) mathcomp(mpoly) tools partition ordtype antisym Schur_mpoly Schur_altdef sympoly homogsym permcent