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I am reading the paper "RingCT 3.0 for Blockchain Confidential Transaction: Shorter Size and Stronger Security" (https://eprint.iacr.org/2019/508.pdf), an improvement to Ring Confidential Transactions.

However, I am having trouble understanding the first security proof (page 17, the definition is in page 8). Can someone help me out, please? In particular I'm looking for some intution on the proof (with a reduced amount of mathematical notation).

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