Section PgroupProps.
Variable gT : finGroupType.
Implicit Types (pi rho : nat_pred) (p : nat).
Implicit Types (x y z : gT) (A B C D : {set gT}) (G H K P Q R : {group gT}).

Lemma pHallJ2 pi G H x : pi.-Hall(G :^ x) (H :^ x) = pi.-Hall(G) H.