random variable that counts the number of steps
from $X$ until we reach a configuration where
$\ell$ is fair. More formally
-$$S_{X,\ell}=\min \{t \geq 1\mid h(X_{t-1})\neq \ell\text{ and }Z_t=(\ell,\.)\text{ and } X_0=X\}.$$
+$$S_{X,\ell}=\min \{t \geq 1\mid h(X_{t-1})\neq \ell\text{ and }Z_t=(\ell,.)\text{ and } X_0=X\}.$$
We denote by
$$\lambda_h=\max_{X,\ell} S_{X,\ell}.$$
\begin{Lemma}\label{prop:lambda}
-If $\ov{h}$ is a square-free bijective function, then one has $E[\lambda_h]\leq 8n^2.$
+If $\ov{h}$ is a square-free bijective function, then the inequality
+$E[\lambda_h]\leq 8n^2$ is established.
+
\end{Lemma}
\begin{proof}
