proposition: Lemma filter_gt_RS (d : unit) (T : inhOrderType d) (w : seq T) n : RS (filter (>%O n) w) = filter_gt_tab n (RS w).
proof: Proof. Proof using . apply/eqP. rewrite -(RS_tabE (is_tableau_filter_gt _ (is_tableau_RS w))) -plactic_RS /=. rewrite to_word_filter_nnil -filter_to_word. apply: plactic_filter_gt; exact: congr_RS. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun ssrnat eqtype finfun fintype choice) mathcomp(order seq tuple finset perm binomial bigop) tools vectNK subseq partition Yamanouchi ordtype std tableau stdtab Schensted plactic Greene_inv stdplact