(* 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).(* 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).(* 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).

(* Specifications: *)
Theorem is_prefix_refl : forall l, is_prefix l l.