proposition: Fact omegasf_is_symmetric p : (sympolyf p) \mPo [tuple sympol 'h_i.+1 | i < n] \is @symmetric n R.
proof: Proof. rewrite comp_mpolyE; apply: rpred_sum => mon _; apply: rpredZ. apply: rpred_prod => i _; rewrite tnth_mktuple. by apply: rpredX; apply: sympolP. 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