proposition: Lemma Frattini_continuous (rT : finGroupType) G (f : {morphism G >-> rT}) : f @* 'Phi(G) \subset 'Phi(f @* G).
proof: Proof. apply/bigcapsP=> M maxM; rewrite sub_morphim_pre ?Phi_sub // bigcap_inf //. have {2}<-: f @*^-1 (f @* G) = G by rewrite morphimGK ?subsetIl. by rewrite morphpre_maximal_eq ?maxM //; case/maximal_eqP: maxM. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(div fintype finfun bigop finset prime binomial) mathcomp(fingroup morphism perm automorphism quotient) mathcomp(action commutator gproduct gfunctor ssralg) mathcomp(countalg finalg zmodp cyclic pgroup center gseries) mathcomp(nilpotent sylow abelian finmodule)