Bell's theorem - for or against Hidden Variables?

[FrediFizzx]

Sorry, no, nobody has ever been interested in this trivial inequality.  And therefore it is completely irrelevant what you tell us about this inequality.  Name it FrediFizzx-inequality and be happy with it.

If nobody has been interested in that inequality, then why is it that it is the one that QM and the experiments all use?

Anyways, you should just admit that you can't demonstrate exactly how QM or the experiments violate any of the Bell inequalities.  It is quite simple math to show that it is impossible for anything including QM, experiments and LHV models to violate the Bell inequalities.