 The proofs of these facts are also straightforward upon appeal to Church’s Thesis. For instance, if \(\textrm{dom}(\phi_i) = A\) and \(\textrm{dom}(\phi_j) = B\) then \(\textit{un}(i,j)\) can be taken to be an index for a program which simulates the computation of \(\phi_i(n)\) and \(\phi_j(n)\) in alternate stages and halts just in case one of these subcomputations halt. Note also that if \(A = W_i\) is computable, then \(\chi_{\overline{A}}(x) = 1 \dotminus \chi_A(x)\) is also computable, from which it follows that \(\overline{A}\) is  computable.[21] 