proposition: Lemma nth_std_pos s i x : is_std s -> i < size s -> i != posbig s -> nth x s i < (size s).-1.
proof: Proof. case: s => [// | s0 s] Hstd Hi Hipos. rewrite [nth _ _ _ < _]ltn_neqAle -ltnS; apply/andP; split. - rewrite /= -(std_max Hstd) -(nth_posbig inh s0 s). rewrite (set_nth_default inh x Hi). by rewrite (nth_uniq _ Hi (posbig_size_cons s0 s) (std_uniq Hstd)). - rewrite -[(size (s0 :: s)).-1.+1]/(size (s0 :: s)). by rewrite -(mem_std _ Hstd); exact: mem_nth. Qed.
imports: mathcomp(all_ssreflect) mathcomp(perm fingroup) tools combclass ordcast partition Yamanouchi ordtype std tableau stdtab sorted Schensted congr plactic Greene Greene_inv