unfold nsearch_spec in |- *.
intros goal work ds ni ai a context complete sound mon.
apply NSearch_Res with ni; try assumption.
apply le_ni_refl.
apply NDerivable.
elim (sound NFalsum).
intros t der_t.
apply Derivable_Intro with (Efq t (Atom goal)).
apply ByAbsurdity; assumption.
apply in_ngamma_cons_work_head.
Qed.

(* Specifications: *)
Lemma contradiction_atoms :
forall (goal i : Int) (work : nf_list) (ds : disjs)
(ni : nested_imps) (ai : atomic_imps) (a : atoms)
(context : flist),
LOOKUP unit i a tt ->
nsearch_spec goal work ds ni ai a context ->
nsearch_spec goal (NAtom i :: work) ds ni ai a context.