The only nullable pairs of nonterminals in G prefix will then be of the form .
because of reduction, properness and consistency of G we have: because of the structure of the grammar transformation by which G prefix was obtained from G, we also have: pairs of occurrences of A ε 1 and A ε 2 with the same index in synchronous rules of G prefix can be systematically removed without affecting the probability of the resulting rule, as outlined in section 3.