proposition: Lemma pcore_setI_normal pi G H : H <| G -> 'O_pi(G) :&: H = 'O_pi(H).
proof: Proof. move=> nsHG; apply/eqP; rewrite eqEsubset subsetI pcore_sub setIC. rewrite !pcore_max ?(pgroupS (subsetIr H _)) ?pcore_pgroup ?gFnormal_trans //=. by rewrite norm_normalI ?gFnorm_trans ?normsG ?normal_sub. 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)