proposition: Lemma mmax_exists H : H \proper G -> {M | M \in 'M(H)}.
proof: Proof. case/(@maxgroup_exists _ (fun M => M \proper G)) => M maxM sHM. by exists M; rewrite !inE sHM andbT. Qed.
imports: HB(structures) mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun eqtype ssrnat seq div choice fintype bigop) mathcomp(finset prime fingroup morphism automorphism action quotient) mathcomp(gfunctor cyclic pgroup center commutator gseries nilpotent) mathcomp(sylow abelian maximal hall) odd_order(BGsection1 BGsection6)