Section Frattini2.
Variables gT : finGroupType.
Implicit Type G : {group gT}.

(* Specifications: *)
Lemma Phi_quotient_id G : 'Phi (G / 'Phi(G)) = 1.
Lemma Phi_quotient_cyclic G : cyclic (G / 'Phi(G)) -> cyclic G.
Variables (p : nat) (P : {group gT}).
Lemma trivg_Phi : p.-group P -> ('Phi(P) == 1) = p.-abelem P.
End Frattini2.