Ltac etac :=
match goal with
| H: interp EE _ |- _ => inv H
| H: InA _ _ nil |- _ => inv H
| H: false = true |- _ => inv H
| H: true = false |- _ => inv H
| _ => auto
end.

Lemma interp_member:
forall x t,
searchtree None None t ->
(member x t = true <-> interp t x).