intros work ds ni i b bs ai ai' a c lookup equiv_ins in_ngamma0.
elim (in_ngamma_cons_work_rev (AImp i b) work ds ni ai a c in_ngamma0);
clear in_ngamma0.
intros in_ngamma0.
apply in_ngamma_ins_ai_tail with i b ai; assumption.
intros eq_c;  rewrite eq_c.
apply in_ngamma_ins_ai_head_old with bs ai; assumption.
Qed.

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