I am a university student in Japan ,and study mathematics.
I can't understand below
"As each Euclidean line $L_\alpha$ of $B^n$ is mapped by $\phi$ onto a hyperbolic line $\phi (L_\alpha)$ of $B^n$ whose endpoints are a distance at most $r$ from those of $L_\alpha$, the Euclidean cylinder $C_\alpha$ with axis $L_\alpha$ and radius $r$ containts $\phi (L_\alpha)$."
Note, $\phi \in M(B^n):=\{\phi \ \ is\ \ a\ Mobius\ \ transformation \ |\ \phi (B^n)=B^n\}$
Of course, I understand $\phi(L)$ is a hyperbolic line. But I cannot prove "the Euclidean cylinder $C_\alpha$ with axis $L_\alpha$ and radius $r$ containts $\phi (L_\alpha)$".