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