intros i j work ds ni ai a c in_ngamma0.
elim (in_ngamma_cons_ds_rev work i j ds ni ai a c in_ngamma0);
clear in_ngamma0.
intros in_ngamma0.
apply in_ngamma_cons_work_tail; assumption.
intros eq_c;  rewrite eq_c.
apply in_ngamma_cons_work_head with (c := NDisj i j).
Qed.

Lemma in_ngamma_shift_work_ni :
forall (x : nested_imp) (work : nf_list) (ds : disjs)
(ni : nested_imps) (ai : atomic_imps) (a : atoms)
(c : normal_form),
in_ngamma (NImp_NF (nested_imp2nimp x) :: work) ds ni ai a c ->
in_ngamma work ds (x :: ni) ai a c.