Ltac delete_emp_in_SEP :=
 repeat
 match goal with |- context [SEPx ?R] =>
   match R with context [emp:: ?R'] =>
     rewrite (delete_emp_in_SEP (length R - S (length R')) R) by reflexivity;
     simpl length; simpl minus; unfold firstn, app, list_drop; fold app
   end
 end.Ltac move_from_SEP :=
  (* combines extract_exists_in_SEP, move_prop_from_SEP, (*move_local_from_SEP, *)
                  flatten_sepcon_in_SEP *)
match goal with |- context [PROPx _ (LOCALx _ (SEPx ?R))] =>
  match R with
  | context [(prop ?P1 && ?Rn) :: ?R'] =>
      let n := length_of R in let n' := length_of R' in
        rewrite (extract_prop_in_SEP (n-S n')%nat P1 Rn) by reflexivity;
        simpl minus; unfold replace_nth (*;
        try (apply semax_extract_PROP; intro)*)
  | context [ exp ?z :: _] =>
        let n := find_in_list (exp z) R
         in rewrite (grab_nth_SEP n); unfold nth, delete_nth; rewrite extract_exists_in_SEP;
             repeat_extract_exists_pre
  | context [ (sepcon ?x  ?y) :: ?R'] =>
        let n := length_of R in let n' := length_of R' in
         rewrite (grab_nth_SEP (n-S n')); simpl minus; unfold nth, delete_nth;
         rewrite flatten_sepcon_in_SEP
 end
end.

(* Specifications: *)
Lemma in_nth_error: forall {A} (x: A) xs, In x xs -> exists n, nth_error xs n = Some x.
Lemma lower_TT: forall rho, @TT (environ->mpred) _ rho = @TT mpred Nveric.
Lemma lower_FF: forall rho, @FF (environ->mpred) _ rho = @FF mpred Nveric.