Alternative Relaxed Target Theorem

We may replace the target theorem (2) (Item 5) by the following alternative target theorem:

$$(u[s({\bf t_1}) \oplus (switchbit({\bf t_1})=\lq 1\textrm{'}), ... ... \oplus (switchbit({\bf t_1})=\lq 0\textrm{'}), Env({\bf t_1})] )$$ (3)

The only difference to the original target theorem (2) is that the ``$>$'' sign became a ``$\geq$'' sign. That is, the Gödel machine will change itself as soon as it has found a proof that the change will not make things worse. A Global Optimality Theorem similar to Theorem 4.1 holds; simply replace the last phrase in Theorem 4.1 by: the utility of starting the execution of the present switchprog is at least as high as the utility of waiting for the proof searcher to produce an alternative switchprog later.