proposition: Lemma eq_uniq_mmax U M H : 'M(U) = [set M] -> H \in 'M -> U \subset H -> H :=: M.
proof: Proof. by move=> uU_M maxH sUH; apply/congr_group/set1P; rewrite -uU_M inE maxH. 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)