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

Lemma in_ngamma_cons_ni_head :
forall (work : nf_list) (ds : disjs) (x : nested_imp)
(ni : nested_imps) (ai : atomic_imps) (a : atoms),
in_ngamma work ds (x :: ni) ai a (NImp_NF (nested_imp2nimp x)).