intros bs work ds ni ai a c in_ngamma0.
elim in_ngamma0; clear in_ngamma0 c.
intros n c0 nth.
elim (inv_nth_app normal_form n bs work c0 nth); clear nth.
intros nth0; right; exists n; assumption.
intros n' nth1; left; apply In_Work with n'; assumption.
intros n i j nth; left; apply In_Disjs with n; assumption.
intros n x nth; left; apply In_Nested_Imps with n; assumption.
intros i b n bs' lookup nth; left; apply In_Atomic_Imps with n bs';
assumption.
intros i lookup; left; apply In_Atoms; assumption.
Qed.

(* Specifications: *)
Lemma in_ngamma_cons_work_rev :
forall (c0 : normal_form) (work : nf_list) (ds : disjs)
(ni : nested_imps) (ai : atomic_imps) (a : atoms)
(c : normal_form),
in_ngamma (c0 :: work) ds ni ai a c ->
in_ngamma work ds ni ai a c + {c = c0}.