The proof is left as an exercise for the reader ;-)
Seriously, I can’t explain the whole chain of thought to you. I made my claim that MWI is implicitly PoC and is a rejection of science and amounts to a supernatural theory. I gave examples of the difference between implicit and explicit PoC errors and gave an historical example where philosophy got hung up on an implicit error. I also cited Jaynes’ argument on how traditional probability theory (on which QM rests) projects probabilities onto reality when they are in fact epistemological measures. And I gave an example of how to use principles to avoid unnecessary work such as examining every single case of perpetual motion. And finally I explained that I am not a physicist and have no obligation or desire to find the specific error.
However, if you decide to do the proof as an excersise I will add the following as a hint;
We have this great theory in QM that allows us to make all kinds of calculations and prediction in the microscopic world. It does not integrate with our best theory of the macroscopic world and cosmology—Special and General Relativity. Moreover, there are various “interpretations” of QM that do not change the calcs but are an attempt to bring meaning and understanding to QM. But they all fail in various ways leaving use with unsatisfactory and contradictory choices between causality -vs- acausality, locality -vs- non-locality, faster than light -vs- c as a limit, one reality -vs- many realities, etc.
Nevetheless, I think these different interpretations of QM should be studied because such understanding and perspectives will lead someone to finding the error that gives rise to all the contradictions and false-alternative. Finally, I don’t need to be a physicist nor find the specific error to state with certainty that either QM or GR (or both) are wrong and that the answer, whatever that turns out to be, will be consistent with both of these theories.
Read this, and then come back and tell us where the reasoning requires PoC.