End PgroupProps.
Arguments pgroupP {gT pi G}.
Arguments constt1P {gT pi x}.
Section NormalHall.
Variables (gT : finGroupType) (pi : nat_pred).
Implicit Types G H K : {group gT}.

Lemma setI_normal_Hall G H K :
H <| G -> pi.-Hall(G) H -> K \subset G -> pi.-Hall(K) (H :&: K).