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 morph_p_elt pi x : x \in D -> pi.-elt x -> pi.-elt (f x).
End Morphim.