Section Pquotient.
Variables (pi : nat_pred) (gT : finGroupType) (p : nat) (G H K : {group gT}).
Hypothesis piK : pi.-group K.

(* Specifications: *)
Lemma quotient_pgroup : pi.-group (K / H). Proof. exact: morphim_pgroup. Qed.
Lemma quotient_pHall :
K \subset 'N(H) -> pi.-Hall(G) K -> pi.-Hall(G / H) (K / H).
Lemma ltn_log_quotient :
p.-group G -> H :!=: 1 -> H \subset G -> logn p #|G / H| < logn p #|G|.