if someone could tell me if I did anything wrong, or could do anything better with this problem please let me know
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Looks good. Though if you just want to present the proof, all that scrapwork isn't necessary and you simply start from "Given , Let ..." and so on.
One thing to note:
and sorry, but if you don't mind, I understand your note but how is it helpful here?
Assuming , we get not
ahh, i see now
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