intros work ds ni ai i a a' equiv_ins.
apply In_Atoms.
generalize equiv_ins; clear equiv_ins.
elim a; clear a; intros t avl_t.
elim a'; clear a'; intros t' avl_t'.
simpl in |- *.
elim (lookup_dec unit i t avl_t).
intros.
inversion_clear equiv_ins.
apply H with d.
apply equal_refl.
assumption.
intros.
inversion_clear equiv_ins.
apply H0.
apply equal_refl.
assumption.
Qed.

Lemma in_ngamma_ins_a_rev :
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 work ds ni ai a c + {c = NAtom i}.