intros work ds x ni1 ni2 ai a.
apply In_Nested_Imps with (n := length ni1) (x := nested_imp2nimp x).
rewrite (nested_imps2nimps_app ni1 (x :: ni2)).
rewrite (nested_imps2nimps_length ni1).
rewrite <- (plus_O (length (nested_imps2nimps ni1))).
apply nth_app1.
simpl in |- *; apply My_NthO.
Qed.

(* Specifications: *)
Lemma in_ngamma_ni_x_ni_tail :
forall (work : nf_list) (ds : disjs) (x : nested_imp)
(ni1 ni2 : nested_imps) (ai : atomic_imps) (a : atoms)
(c : normal_form),
in_ngamma work ds (ni1 ++ ni2) ai a c ->
in_ngamma work ds (ni1 ++ x :: ni2) ai a c.