proposition: Lemma syms_symm_partdom la : 's[la] = 'm[la] + \sum_(mu | (mu < la :> 'PDom_d)%O) 'K(la, mu) *: 'm[mu] :> SF.
proof: Proof. rewrite -(map_syms intr) syms_symm_partdom_int. rewrite rmorphD rmorph_sum /= map_symm; congr (_ + _); apply eq_bigr => i _. rewrite linearZ_LR /= map_symm /=; congr (_ *: _). by rewrite mulrz_nat. 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