Tactic Notation "freeze1_SEP" constr(n) constr(m) :=
(gather_SEP n m); eapply (freeze1_SEP' (nat_of_Z 0)); simpl.
Tactic Notation "freeze1_SEP" constr(n) constr(m) constr(k)  :=
(gather_SEP n m k); eapply (freeze1_SEP' (nat_of_Z 0)); simpl.
Tactic Notation "freeze1_SEP" constr(n) constr(m) constr(k)  constr(p) :=
(gather_SEP n m k p); eapply (freeze1_SEP' (nat_of_Z 0)); simpl.
Tactic Notation "freeze1_SEP" constr(n) constr(m) constr(k) constr(p) constr(q) :=
(gather_SEP n m k p q); eapply (freeze1_SEP' (nat_of_Z 0)); simpl.
(*******************freezing a list of mpreds ******************************)
Fixpoint freezelist_nth (l: list nat) (al: list mpred): (list mpred) * (list mpred) :=
match l with
| nil => (nil,al)
| (n::l') => let (xs, ys) := freezelist_nth l' al
in (nth n ys emp::xs, delete_nth n ys)
end.

Lemma map_delete_nth {A B} (f:A->B): forall n l, delete_nth n (map f l) = map f (delete_nth n l).
Fixpoint my_nth {A} (n : nat) (l : list A) (default : A) {struct l} : A :=
match n with
| 0%nat => match l with
| [] => default
| x :: _ => x
end
| S m => match l with
| [] => default
| _ :: t => my_nth m t default
end
end.