Apply SCAN to the single terminal edge that makes up G to obtain [b(G), q : X → G • , φ q ] and finally apply COMPLETE to this and the axiom reach the goal Only if: Assume the goal can be reached from the axiom and G = e. Then the item [b(e), q : X → e, φ q ] must have been reached at some point for some q ∈ P G .
q : X → e is a production and so e = G ∈ L X (G).