Understanding Rabin's Diminishing Marginal Utility of Wealth Cannot Explain Risk Aversion
From $U(W+11)−U(W)\le U(W)−U(W−10)$ we get that $\frac{U(W+11)-U(W)}{11}\le\frac{10}{11}\frac{U(W)-U(W-10)}{10}$, which is what the sentence before the bolded italic part says.

Now by concavity of $U(.)$ we know that $MU(W-10)\ge\frac{U(W)-U(W-10)}{10}$, and also that $MU(W+11)\le\frac{U(W+11)-U(W)}{11}$.

Therefore $MU(W+11)\le\frac{U(W+11)-U(W)}{11}\le\frac{10}{11}\frac{U(W)-U(W-10)}{10}\le\frac{10}{11}MU(W-10)$.

So $MU(W+11)\le\frac{10}{11}MU(W-10)$, wich is just the bolded italic statement.