induction 1; intuition; simpl in *.
destruct H.
subst.
eapply in_app_or in H1.
intuition.
eapply in_or_app.
left.
eapply firstn_In.
eauto.
Qed.

Theorem firstn_NoDup :
forall (A : Type) n (ls : list A),
NoDup ls ->
NoDup (firstn n ls).