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 normal_max_pgroup_Hall G H :
[max H | pi.-subgroup(G) H] -> H <| G -> pi.-Hall(G) H.