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 union'_spec : forall s s' x, valid s -> valid s' ->
(interp (union' s s') x <-> interp s x \/ interp s' x).