proposition: Lemma symh_to_symp_intpartn n : [char R] =i pred0 -> 'h_n = \sum_(l : 'P_n) (\sum_(c : intcompn n | perm_eq l c) \Pi c) *: 'p[l] :> SF.
proof: Proof. move/symh_to_symp_prod_partsum => ->. rewrite (partition_big (@partn_of_compn n) xpredT) //=. apply eq_bigr => l _; rewrite scaler_suml; apply eq_big. - move=> c; apply/eqP/idP => [<- | Hperm]; first by rewrite /partn_of_compn /= perm_sort. apply val_inj => /=; apply (sorted_eq geq_trans) => //. by rewrite (permPr Hperm) perm_sort. - move=> c /eqP <-; congr (_ *: _). rewrite /prod_symp /prod_gen; apply: perm_big. by rewrite /partn_of_compn perm_sym /= perm_sort. Qed.
imports: HB(structures) mathcomp(all_ssreflect) mathcomp(ssralg ssrint fingroup perm) mathcomp(ssrcomplements freeg mpoly) sorted tools ordtype permuted partition skewpart composition Yamanouchi std tableau stdtab skewtab permcent antisym Schur_mpoly therule Schur_altdef unitriginv