proposition: Lemma eq_Hall_pcore G H : pi.-Hall(G) 'O_pi(G) -> pi.-Hall(G) H -> H :=: 'O_pi(G).
proof: Proof. move=> hallGpi hallH. exact: uniq_normal_Hall (pcore_normal G) (Hall_max 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)