intros c0 work ds ni ai a c in_ngamma0.
elim in_ngamma0; clear in_ngamma0 c.
intros n a0 nth; apply In_Work with (S n); apply My_NthS; assumption.
intros n i j nth; apply In_Disjs with n; assumption.
intros n x nth; apply In_Nested_Imps with n; assumption.
intros i b n bs lookup nth; apply In_Atomic_Imps with n bs; assumption.
intros i lookup; apply In_Atoms; assumption.
Qed.

(* Specifications: *)
Lemma in_ngamma_cons_work_head :
forall (c : normal_form) (work : nf_list) (ds : disjs)
(ni : nested_imps) (ai : atomic_imps) (a : atoms),
in_ngamma (c :: work) ds ni ai a c.