intros work ds ni i b ai ai' a notlookup equiv_ins.
apply In_Atomic_Imps with 0 (b :: nf_nil).
generalize equiv_ins notlookup; clear equiv_ins notlookup.
elim ai; clear ai; intros t avl_t.
elim ai'; clear ai'; intros t' avl_t'.
simpl in |- *.
intros.
inversion_clear equiv_ins.
clear H1 H2.
apply H0.
apply equal_refl.
assumption.
apply My_NthO.
Qed.

(* Specifications: *)
Lemma in_ngamma_ins_ai_head_old :
forall (work : nf_list) (ds : disjs) (ni : nested_imps)
(i : Int) (b : normal_form) (bs : nf_list) (ai ai' : atomic_imps)
(a : atoms),
LOOKUP nf_list i ai bs ->
EQUIV_INS nf_list i (cons b) nf_nil ai ai' ->
in_ngamma work ds ni ai' a (AImp i b).