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 psubgroupJ pi G H x :
x \in G -> pi.-subgroup(G) (H :^ x) = pi.-subgroup(G) H.