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_p_index pi G H :
H \subset D -> pi.-nat #|G : H| -> pi.-nat #|f @* G : f @* H|.