Section SomeHall.
Variable gT : finGroupType.
Implicit Types (p : nat) (pi : nat_pred) (G H K P R : {group gT}).

Lemma Hall_psubJ p pi G H P :
pi.-Hall(G) H -> p \in pi -> P \subset G -> p.-group P ->
exists2 x, x \in G & P \subset H :^ x.