By triangle inequality, it is clear that for any probabilistic polynomial time algorithm A, .
\mathsf{Adv}_{D_1, D_2}^{\mathsf{dist}}(\mathbf{A}) \leq \sum_{i=0}^{t-1}\mathsf{Adv}_{H_i, H_{i+1}}^{\mathsf{dist}}(\mathbf{A}).