Theorem 7.1.6 is stated as below.
With probability one, Brownian paths are not Lipschitz continuous (and hence not differentiable) at any point
$$Y_{k,n}=\max\left\{\left|B(\frac{k+j}{n})-B(\frac{k+j-1}{n})\right|:j=0,1,2\right\}$$ $$B_n=\{\text{at least one }Y_{k,n}\leq5C/n \}$$
and what I can't understand is the second inequality in the proof. $$P(A_n)\leq P(B_n)\leq n P(|B(1/n)|\leq5C/n)^3$$ How does this inequality hold?