Tuliskan \(u_i=|x_i-y_i|\text{.}\) Karena \(\max_i u_i^2\leq\sum_i u_i^2\text{,}\) diperoleh \(d_M\leq d_E\text{.}\) Karena \((\sum_i u_i)^2=\sum_i u_i^2+2\sum_{i<j}u_i u_j\geq\sum_i u_i^2\text{,}\) diperoleh \(d_E\leq d_T\text{.}\) Cauchy–Schwarz memberi \(\sum_i u_i\leq\sqrt{\sum_i u_i^2}\sqrt{\sum_i1^2}=\sqrt n\,d_E\text{.}\)

Jika \(d_T(a,x)<r\text{,}\) maka \(d_E(a,x)<r\text{,}\) lalu \(d_M(a,x)<r\text{;}\) ini memberi tiga inklusi pertama. Jika \(d_E(a,x)<r/\sqrt n\text{,}\) maka \(d_T(a,x)\leq\sqrt n\,d_E(a,x)<r\text{,}\) memberi inklusi terakhir.