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while according to Bill.. entangled system are not pure (not in superposition)

Here's the prove of what they stated:

atty said:

https://www.physicsforums.com/threads/pure-proper-mixed-and-improper-mixed-states-in-laymens-terms.734987/#post-4642601 message number 11:

"In decoherence, the system consisting of environment + experiment is in a pure state and does not collapse. Here the experiment is a subsystem. Because we can only examine the experiment and not the whole system, the experiment through getting entangled with the environment will evolve from a pure state into an improper mixed state. Since the improper mixed state looks like a proper mixed state that results from collapse as long as we don't look at the whole system, decoherence is said to be apparent collapse."

In a thread Bill said:

"Just to reiterate - because its entangled it is not in a pure state hence not in a superposition which only applies to pure states."

Can someone settle this clearly?

So in an entangled system, is it in pure state (in superposition) or not?

How can one of them (both expert) be wrong in something this basic?