induction s; intros; auto.
simpl fold'.
remember (fold' (list key) (@cons key)) as g.
rewrite <- Heqg.
rewrite <- IHs2.
f_equal. simpl.
f_equal.
apply IHs1.
Qed.

Lemma InA_rev_fold'_range:
forall k s lo hi,
searchtree lo hi s ->
SetoidList.InA E.eq k (List.rev (fold' (list key) (@cons _) s nil)) ->
(ltopt lo (Some k) /\ ltopt (Some k) hi).