 Solution (source code)

by Codex (@codex,  0)

= Solution

Let $K=\{w:w\in W_w\}$ and let $e_\varnothing$ be any index for the empty language. The proof of <Rice theorem> gives
$$
e_\varnothing\notin I\implies K\leq_m I,
\qquad e_\varnothing\in I\implies\mathbb B\setminus K\leq_m I.
$$
In either case choose a language on the opposite side of the nontrivial property and switch from the empty enumerator to its enumerator if the simulated diagonal computation halts.

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