proposition: Lemma syms_symsM d1 (la : 'P_d1) d2 (mu : 'P_d2) : 's[la] * 's[mu] = \sum_(nu : 'P_(d1 + d2) | included la nu) 's[nu] *+ LRyam_coeff la mu nu :> SF.
proof: Proof. apply val_inj; rewrite /= LRyam_coeffP linear_sum /=. by under [RHS]eq_bigr do rewrite raddfMn. 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