# real analysis – Normalized spaces. Prove that if one closed ball nested into other one, then \$r_1 leq r_2 – ||x_1-x_2||\$

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.