intros c work ds ni ai a context sound.
unfold nsound in |- *.
intros c0 in_gamma.
elim (in_ngamma_cons_work_rev c work ds ni ai a c0 in_gamma); clear in_gamma.
intros in_gamma.
apply derivable_weak.
apply sound; assumption.
intros eq;  rewrite eq; clear eq.
apply Derivable_Intro with (Var 0).
apply ByAssumption.
apply My_NthO.
Qed.
(**********************************************************************)

(* Specifications: *)
Lemma nsound_cons_work_weak :
forall (b c : normal_form) (work : nf_list) (ds : disjs)
(ni : nested_imps) (ai : atomic_imps) (a : atoms)
(context : flist),
(Derivable context (nf2form b) -> Derivable context (nf2form c)) ->
nsound (b :: work) ds ni ai a context ->
nsound (c :: work) ds ni ai a context.