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 elements'_interp : forall s x l,
SetoidList.InA E.eq x (elements' s l) <-> interp s x \/ InA E.eq x l.