Function_Obtained_by_Minimization_from_URM_Computable_Relations

Let $\mathcal R$ be a URM computable $k+1$-ary relation on $\N^{k+1}$. Let the function $f: \N^{k+1} \to \N$ be a URM computable function. Let $g: \N^k \to \N$ be the function obtained by minimization from $f$ thus $g \left({n_1, n_2, \ldots, n_k}\right) \approx \mu y \mathcal R \left({n_1, n_2, \ldots, n_k, y}\right)$ Then $g$ is also URM computable.