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 eq_in_pHall pi rho G H :
{in \pi(G), pi =i rho} -> pi.-Hall(G) H = rho.-Hall(G) H.