proposition: Lemma omegasf_prodsymp la : head 0%N la <= n -> omegasf 'p[la] = (-1) ^+ (d - size la) *: 'p[la].
proof: Proof. move=> Hhead. rewrite /prod_symp /prod_gen rmorph_prod /= exp1sumnDsize. rewrite -scaler_prod !big_seq. apply: eq_bigr => i Hin; rewrite omegasf_symp //. rewrite lt0n (in_part_non0 _ Hin) //=. exact: (leq_trans (intpartn_leq_head Hin) Hhead). 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