 These biconditionals hold because \(\phi_i(n) \darrow\) just in case \(\phi_{s^2_1(i,n)}(y)\) is \(\const_1(x)\) (i.e., the constant 1-function) as opposed to the everywhere undefined function just in case \(\phi_{s^2_1(i,n)}(s^2_1(i,n)) \darrow\). But as the later condition is equivalent to \(s^2_1(i,n) \in K\), \(s^2_1(i,x)\) is a many-one reduction showing \(A \leq_m K\).