End NormalHall.
Section Morphim.
Variables (aT rT : finGroupType) (D : {group aT}) (f : {morphism D >-> rT}).
Implicit Types (pi : nat_pred) (G H P : {group aT}).

Lemma morphim_pSylow p G P :
P \subset D -> p.-Sylow(G) P -> p.-Sylow(f @* G) (f @* P).