proposition: Lemma pcore_normal G : 'O_pi(G) <| G.
proof: Proof. rewrite /(_ <| G) pcore_sub; apply/subsetP=> x Gx. rewrite inE; apply/bigcapsP=> M maxM; rewrite sub_conjg. by apply: bigcap_inf; apply: max_pgroupJ; rewrite ?groupV. 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)