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 pHallE pi G H : pi.-Hall(G) H = (H \subset G) && (#|H| == #|G|`_pi).