Section Frattini.
Variables gT : finGroupType.
Implicit Type G M : {group gT}.

(* Specifications: *)
Lemma Phi_sub G : 'Phi(G) \subset G.
Lemma Phi_nongen G X : 'Phi(G) <*> X = G -> <<X>> = G.
Lemma Frattini_continuous (rT : finGroupType) G (f : {morphism G >-> rT}) :
f @* 'Phi(G) \subset 'Phi(f @* G).