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 interp_dec: forall s x, {interp s x}+{~interp s x}.
Definition lt' (s s': tree):  Prop :=  compare' s s' = Lt.