proposition: Lemma maxgroup_exists : {H : {group gT} | maxgroup H gP & G \subset H}.
proof: Proof. have [A maxA sGA]: {A | maxgroup A gP & G \subset A}. by apply: maxset_exists; rewrite groupP genGidG. by exists <<A>>%G; rewrite /= gen_set_id; case/andP: (maxsetp maxA). Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)