\[\begin{aligned} \text{diam}(i',j') &\leq \frac{2}{s}|i,j| + L_r + \frac{2}{s}|i,j| + R_r + (1 + \frac{4}{s}) |i,j|\\ &= |i,j| \left( \frac{2}{s} + \frac{2}{s} + 1 + \frac{4}{s} \right) + L_r + R_r \\ &= \frac{s+8}{s} |i,j| + L_r + R_r \\ &\leq \frac{s+8}{s}\left(|i,j| + L_r + R_r\right)\\ &= \left(1 + \frac{8}{s}\right) \text{diam}(i,j)\end{aligned}\]