proposition: Lemma rembig_plact2 u v : u \in (plact2 v) -> rembig u = rembig v.
proof: Proof. Proof using. move/plact2P => [a] [b] [c] [] /andP[Hab Hbc] -> -> /=. rewrite Hab [(c < b)%O]ltNge Hbc /= !andbT. by rewrite [(c < a)%O]ltNge (lt_le_trans Hab Hbc) (ltW (lt_le_trans Hab Hbc)). Qed.
imports: mathcomp(all_ssreflect) mathcomp(perm) tools partition ordtype tableau stdtab Schensted congr