GH-convergence of CAT$(0)$-spaces: stability of the Euclidean factor

We prove that if a sequence of geodesically complete CAT$(0)$-spaces $X_j$ with uniformly cocompact discrete groups of isometries converges in the Gromov-Hausdorff sense to $X_{\mathrm{\infty }}$, then the dimension of the maximal Euclidean factor splitted off by $X_{\mathrm{\infty }}$ and $X_j$ is the same, for $j$ big enough. In other words, no additional Euclidean factors can appear in the limit.