proposition: Lemma cover_nil (T : finType) : #|cover [set s : {set T} in [::]]| = 0.
proof: Proof. rewrite set_nil /cover /= big_pred0; last by move=> i /=; rewrite inE. by rewrite cards0. Qed.
imports: mathcomp(all_ssreflect) mathcomp(perm) sorted tools subseq partition tableau Schensted congr plactic ordcast