Inductive interp: tree -> (key -> Prop) :=
| member_here: forall x y c tl tr, K.eq x y -> interp (T c tl y tr) x
| member_left: forall x y c tl tr, interp tl x -> interp (T c tl y tr) x
| member_right: forall x y c tl tr, interp tr x -> interp (T c tl y tr) x.

Lemma interp_empty: forall x, ~ interp EE x.
Hint Constructors interp.