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It seems to me that there is a substantive difference between la and lai only when the name is applied to a group, exactly parallel to le/lei. For example, I can refer distributively to a group of dogs as {le gerku}, or collectively as {lei gerku}, or, if I name the group {gerk}, then distributively as {la gerk} and collectively as {lai gerk}. This has a couple of interesting implications. The first is that la is sensitive to scope relative to le in the way that le is -- i.e. a way that is nonvacuous only when the sumti refers to a nonsingleton group. The second is that {ko'a me la brod} must mean {ro da poi ke'a cmima lai/la'i brod zo'u ko'a me da} (which is unlikely to be something one would want to say). While {ko'a na me la brod} must mean {na ku ro da poi ke'a cmima lai/la'i brod zo'u ko'a me da} which is even less likely to be something one would want to say. I conclude from all of this that {lai} is far less likely than {la} to result in one inadvertently saying something one didn't mean, and this is especially the case after {me}. --And.