apply Corresponding.
+ intros p s Contra.
inversion Contra.
+ intros p InNil. inversion InNil.
+ apply FreeNil.
Qed.
Ltac fireInLeft name :=
match goal with
| [H : In ?X (?X :: ?XS) -> _ |- _ ] =>
assert (In X (X :: XS)) as name by (left; auto); apply H in name; clear H
end.

Lemma corrUndefEmpty : forall l f, correspondingSeedTree l f SeedTreeUndef -> l = [].
intros l f Corr.