proposition: Theorem Pieri_colpartn (P1 : 'P_d1) : Schur P1 * Schur (colpartn d2) = \sum_(P : 'P_(d1 + d2) | vb_strip P1 P) Schur P.
proof: Proof. Proof using . rewrite LRyam_coeffP. rewrite [LHS]big_mkcond [RHS]big_mkcond /=. apply eq_bigr => p _. case: (boolP (included P1 p)) => Hincl; first last. suff /negbTE -> : ~~ vb_strip P1 p by []. move: Hincl; apply contra; exact: vb_strip_included. rewrite (LRyam_coeff_colpartn Hincl). by case: (vb_strip P1 p); rewrite /= ?mulr1n ?mulr0n. Qed.
imports: HB(structures) mathcomp(all_ssreflect) mathcomp(ssralg) mathcomp(mpoly) tools ordcast combclass partition skewpart Yamanouchi ordtype std tableau stdtab Schensted congr plactic Greene_inv stdplact Yam_plact skewtab shuffle Schur_mpoly freeSchur