sigh, those are both typos. I mean P_1 \le R_1 [this is your “Also assume”] and I changed M_{PI} to M in editing - “PI” stood for prefix-intersection.
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sigh, those are both typos. I mean P_1 \le R_1 [this is your “Also assume”] and I changed M_{PI} to M in editing - “PI” stood for prefix-intersection.