# Cardinality of a set of successful hash values

Im trying to comprehend a proof from the paper "Efficient Identity Based Signature Schemes Based on Pairings"(2002) by Florian Hess. At one point of the proof for Theorem 2 I don't understand how the cardinality is concluded. Summarized my problem is the following:
We have a machine C that replays a machine B at most $$\frac{2}{\epsilon_B} + \frac{14n_2}{\epsilon_B}$$ times where $$\epsilon_B$$ is the probability for machine B to suceeds on its own and where $$n_2$$ is the number of queries B asks. By replaying B machine C produces two valid signatures $$(\mu_1,r)$$ and $$(\mu_2,r)$$ with message hash $$h_1(m,r)$$ and $$h_2(m,r)$$ for the same m,r. The first $$\frac{2}{\epsilon_B}$$ are to generate the first signature and the $$\frac{14n_2}{\epsilon_B}$$ replays are to produce the second signature by applying the forking lemma. The forking lemma is applied in regard to a random tape $$\delta \in (\mathbb{Z} / l \mathbb{Z})^\times \times (\mathbb{Z} / l \mathbb{Z})^\times$$ which is used to answer the $$n_2$$ queries for $$h(m,r)$$. Every entry of $$\delta$$ is used as $$(v,w)$$ to answer the queries. The value of $$m,r$$ stays the same up until the point $$\beta$$ where the random tape forks: $$\delta =(\delta_j)$$ for $$j<\beta$$. From this the conclusion is drawn that the $$h_i(m,r)$$ are randomly chosen from the set of successful hash values $$\delta_\beta$$ which has the cardinality $$\geq \frac{\epsilon_B(l-1)^2}{14n_2}$$ (with $$l$$ being the security parameter). Why is the cardinality of this set $$\geq \frac{\epsilon_B(l-1)^2}{14n_2}$$?