> $x->__equals($y) && $y->__equals($z) requires that $x->__compareTo($z) be 
> *TRUE*.

Typo here, it should be __equals at the end not __compareTo.

> In fact, returning 0 in __compareTo for undefined natural ordering leads to 
> all kinds of strange behaviour

If this is the case, I do not understand why you split comparison and equality, 
as I understood it at first the point was exactly to be able to have ordering 
equality without having value equality. If this leads to strangeness, why allow 


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