Universal_URM_Computable_Functions

For each integer $k \ge 1$, there exists a URM computable function $\Phi_k: \N^{k+1} \to \N$ such that for each URM computable function $f: \N^k \to \N$ there exists a natural number $e$ such that $\forall \left({n_1, n_2, \ldots, n_k}\right) \in \N^k: f \left({n_1, n_2, \ldots, n_k}\right) \approx \Phi_k \left({e, n_1, n_2, \ldots, n_k}\right)$. This function $\Phi_k$ is '''universal for URM computable functions of $k$ variables'''.