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).