I am trying to grasp some basic proofs regarding brownian motions. Below the final step in Lévy's construction of Brownian motions from a dyadic grid.
$$ \begin{align*} P(\sup_{t \leq n}{|{W_n(t) - W_{n-1}(t)}| \geq n^{-2})} &\leq n2^{n-1}P(|Z| \geq s^{-1}_nn^{-2}) \\ &\leq n2^{n-1}(s_nn^2)^4E(|Z|^4) \\ &\leq n^92^{-n}E(|Z|^4) \end{align*} $$
$$ \sup_{t \leq n}{|{W_n(t) - W_{n-1}(t)}|} =\max{(|Z|s^{-1})}$$
with $Z \sim \mathcal{N}(0,1)$ and $s^2_n = 2^{-n-1}$.
What inequality is used here? Step $2$ uses Markov, and step $1$ is standardizing $|Z|$ by diving with $s$. Where does though the $n2^{n-1}$ comes from?