proposition: Lemma comp_symbe m (H : mnmwgt m = d) : 'X_[m] \mPo E = 'he[intpartn_of_mon H].
proof: Proof. Proof using. rewrite comp_mpolyX /= /prod_gen /intpartn_of_mon /intpart_of_mon /=. rewrite rmorph_prod /= [RHS](perm_big _ (permEl (perm_rev _))) /=. rewrite big_flatten /= big_map /= -big_enum /=; apply eq_bigr => i _. rewrite big_nseq tnth_mktuple. by rewrite -big_const_ord prodr_const cardT -cardE card_ord. Qed.
imports: HB(structures) mathcomp(all_ssreflect) mathcomp(ssralg matrix vector ssrnum algC archimedean) mathcomp(fingroup perm) mathcomp(ssrcomplements freeg mpoly) tools sorted ordtype permuted partition permcent antisym Schur_mpoly Schur_altdef sympoly