Proof using.
intros c a l; generalize a l; elim c; clear a l c; simpl in |- *; auto.
intros a l H H0; case H0.
intros a; case a.
intros a0 l l0 H a1 l1 H0 H1; case (list_eq_dec eq_bool_dec l1 l).
intros H2; apply f_equal with (f := Some (A:=A)).
case H1; intros H3.
injection H3; auto.
apply unique_prefix1 with (1 := H0) (lb1 := l) (lb2 := l1); simpl in |- *;
auto.
rewrite H2; auto.
intros H2; case H1; auto.
intros H3; case H2; injection H3; auto.
intros; apply H; auto.
apply unique_prefix_inv with (1 := H0); auto.
Qed.
Opaque list_eq_dec.

(* The value of an empty list cannot be found in a non empty code *)
Theorem not_null_find_val :
forall c : code, not_null c -> find_val nil c = None.