intros work ds ni ai i a a' c equiv_ins in_ngamma0.
elim (in_ngamma_cons_work_rev (NAtom i) work ds ni ai a c in_ngamma0);
clear in_ngamma0.
intros in_ngamma0.
apply in_ngamma_ins_a_tail with i a; assumption.
intros eq_c;  rewrite eq_c.
simpl in |- *.
apply in_ngamma_ins_a_head with a; assumption.
Qed.

Lemma in_ngamma_shift_a_work :
forall (work : nf_list) (ds : disjs) (ni : nested_imps)
(ai : atomic_imps) (i : Int) (a a' : atoms) (c : normal_form),
EQUIV_INS unit i (fun _ : unit => tt) tt a a' ->
in_ngamma work ds ni ai a' c -> in_ngamma (NAtom i :: work) ds ni ai a c.