intros t; elim t; simpl in |- *; auto.
intros a a0 H; inversion H; auto.
intros b H b0 H0 a H1; apply in_or_app; inversion H1; auto.
Qed.

(* Specifications: *)
(* An element of a list of all leaves is a leaf *)
Theorem all_leaves_inb : forall t a, In a (all_leaves t) -> inb (leaf a) t.
Proof using.