intros.
simpl.
rewrite (space_denote_permute _ _ H).
trivial.
Qed.

Lemma exorcize_sound_nil:
forall e pnatoms nextv nextv2 sigma0 cl,
Ident.lt nextv nextv2 ->
exorcize e pnatoms sigma0 [ ] nextv = Some cl ->
(assertion_denote (Assertion pnatoms (rev sigma0 ++ [ ]))
|-- fold_right
(fun P => orp (existsv nextv (assertion_denote P))) FF cl) /\
(forall (Q : assertion),
In Q cl ->
(match Q with
|Assertion  _ (Next e0 _ :: _) => e=e0
| _ => False
end /\
fresh freshmax_assertion Q nextv2)).