An isometric embedding of the space of non-increasing sequences with non-negative terms into the Gromov-Hausdorff space

The Gromov-Hausdorff space is a certain metric space induced by the Gromov-Hausdorff convergence, and we study an isometric embedding into this space. While the subspace of non-negative real numbers in the Euclidean space admits an isometric embedding, we prove that the subspace of $\ell^\infty$ consisting of non-increasing sequences with non-negative terms can be isometrically embedded into the Gromov-Hausdorff space.