proposition: Lemma sub_Hall_pcore G K : pi.-Hall(G) 'O_pi(G) -> K \subset G -> (K \subset 'O_pi(G)) = pi.-group K.
proof: Proof. by move=> hallGpi; apply: sub_normal_Hall (pcore_normal G). 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)