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I think that I know the answer to your question, although I have found it a little confusing.

Rawls believes that the 'correct' principles of justice are those that would be chosen in the original position as he defines it.

But the reason he defines the original position the way he does is that he believes that it embodies certain notions of justice widely held in our culture.

And finally, the proof that the original position embodies such widely held notions is that the principles chosen the original position can be easily brought into a reflective equilibrium with our considered judgments about justice.