proposition: Lemma setpart_subset P A : A \in P -> A \subset S.
proof: Proof. have /and3P[/eqP <- _ _ AinP] := setpartP P. rewrite /cover; apply/subsetP=> x xinA. by apply/bigcupP=> /=; exists A. Qed.
imports: HB(structures) mathcomp(all_ssreflect) mathcomp(div ssralg ssrint ssrnum binomial) tools combclass sorted ordtype partition