proposition: Lemma mem_Hall_pcore G x : pi.-Hall(G) 'O_pi(G) -> x \in G -> (x \in 'O_pi(G)) = pi.-elt x.
proof: Proof. by move=> hallGpi; apply: mem_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)