proposition: Lemma Hall_max pi H G : pi.-Hall(G) H -> [max H | pi.-subgroup(G) H].
proof: Proof. move=> hallH; apply/maxgroupP; split=> [|K /andP[sKG piK] sHK]. by rewrite /psubgroup; case/and3P: hallH => ->. exact: (sub_pHall hallH). Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(fintype bigop finset prime fingroup morphism) mathcomp(gfunctor automorphism quotient action gproduct) mathcomp(cyclic)