Let $(X, ||*||)$ normalized spase.

Prove that if one closed ball nested into other one ($overline{B_{r_1}}(x_1) subset overline{B_{r_2}}(x_2))$, then $r_1 leq r_2 -||x_1-x_2||$, where $r_1, r_2$ are radiuses of such balls and $x_1, x_2$ are their centers.