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Why would it not be able to find reductions now, but be able to find them just by being told that P=NP is definitely true?
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From my understanding, the two are equivalent; if you can reduce an NP problem to a P problem, you've proven P=NP. The rest is application.
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Yes but it's also possible that there are other proofs. The point remains, the content of the proof is what matters, not that the statement is proven.
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