intros t; elim t; simpl in |- *; auto with arith.
intros b H b0 H0; rewrite length_app.
replace 0 with (0 + 0); auto with arith.
apply plus_lt_compat.
generalize H; elim (compute_code b); simpl in |- *; auto with arith.
generalize H0; elim (compute_code b0); simpl in |- *; auto with arith.
Qed.
Hint Resolve length_compute_lt_O : core.

(* Specifications: *)
(* If the computed code has a key it was a leaf of the tree *)
Theorem inCompute_inb :
forall (t : btree) (a : A) (l : list bool),
In (a, l) (compute_code t) -> inb (leaf a) t.