proposition: Lemma pi_Msigma : \pi(M`_\sigma) =i \sigma(M).
proof: Proof. move=> p; apply/idP/idP=> [|s_p /=]; first exact: pnatPpi (pcore_pgroup _ _). by rewrite (card_Hall Msigma_Hall) pi_of_part // inE /= sigma_sub_pi. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun eqtype ssrnat seq div path fintype) mathcomp(bigop finset prime fingroup morphism perm automorphism quotient) mathcomp(action gproduct gfunctor pgroup cyclic center commutator) mathcomp(gseries nilpotent sylow abelian maximal hall) odd_order(BGsection1 BGsection3 BGsection4 BGsection5 BGsection6) odd_order(BGsection7 BGsection9)