Then, does {loi broda na} go over to {piro loi broda naku}? Yes, but the reverse does not work, nor does {piro loi broda na} go over to {loi broda naku}. The first works because {piro} is one way of realizing {pisu'o} and we've said that no way of realizing {pisu'o loi broda} is brode, so piro loi broda is not either. To get the right results, we have to view {loi broda} not merely as {piso'u loi broda}, a part of the mass, but recognize that it is one or several such parts, {su'o lo piso'u loi broda}. Shifting negation then works on the outside quantifier only: {loi broda na} is equivalent to {ro lo pisu'o loi broda naku} (and nothing here can be dropped) and {loi broda naku} is equivalent to {ro lo pisuo loi broda na}.
On the other hand, as xorxes says, {piro loi broda} refers (unusually for Lojban) to an individual and thus is transparent to negation: {piro loi broda na} is equivalent to {piro loi broda naku}.
These same manuevers apply regardless of what {pisu'o} and {piro} are applied to (individuals, masses or sets). The move with {pisu'o} applies as well to all cases with "regular" numbers in place of {su'o}, the transformation is on {su'o lo pi-n loi}. (The move from {pi-n l broda na} to {piro l broda naku} does not work of course.
It seems that {loi broda na brode} also implies {pino loi broda cu brode} , which seems to work as {no lo pisu'o loi broda}. But this is open to several possible (but, I think -- and hope -- rejectable) criticisms, so it can be discussed for a while.
And you thought a logical language would have a simple logic!
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