Proof using.
intros l; elim l; simpl in |- *; auto.
intros b; red in |- *; intros a; red in |- *; intros H; inversion H.
intros (a1, l1) l0 H b; apply not_null_cons; auto.
red in |- *; intros; discriminate.
Qed.
Hint Resolve not_null_map : core.
(* Define the property of list of booleans to be a prefix of another *)
Inductive is_prefix : list bool -> list bool -> Prop :=
| prefixNull : forall l, is_prefix nil l
| prefixCons :
forall (b : bool) l1 l2,
is_prefix l1 l2 -> is_prefix (b :: l1) (b :: l2).
Hint Constructors is_prefix : core.

(* Specifications: *)
(* A list is a prefix of itself *)
Theorem is_prefix_refl : forall l, is_prefix l l.
Proof using.