Untuk \(x,y,z\in X\text{,}\) tetapkan \(a_i=d_i(x_i,y_i)\text{,}\) \(b_i=d_i(y_i,z_i)\text{,}\) dan \(c_i=d_i(x_i,z_i)\text{.}\) Maka \(c_i\leq a_i+b_i\text{.}\) Kembangkan \(\sum_i(a_i+b_i)^2\) dan gunakan Cauchy-Schwarz pada \(\sum_i a_ib_i\text{.}\)