proposition: Lemma normal_Hall_pcore H G : pi.-Hall(G) H -> H <| G -> 'O_pi(G) = H.
proof: Proof. move=> hallH nHG; apply/eqP. rewrite eqEsubset (sub_normal_Hall hallH) ?pcore_sub ?pcore_pgroup //=. by rewrite pcore_max //= (pHall_pgroup 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)