Definition union' (s1 s2: tree) : tree :=
match compare_height s1 s1 s2 s2 with
| Lt => fold' _ insert s1 s2
| Gt => fold' _ insert s2 s1
| Eq => linear_union s1 s2
end.

Lemma delmin_eq:
forall s x (v: searchtree None None s),
choose' s = Some x ->
delete'_min s = Some (x, delete x s).