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"There are not $n$ $S$-neighbours $y_1, \dots, y_n$ of $x$ with $C$ in $\mathcal{L}(y_i)$ and $y_i \not = y_j$ for $1 \leq i < j \leq n$."

If there are $n-1$ such $S$-neighbours, is that entailed by this sentence? Or this sentence only entails that there's no such $S$-neighbors?

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    If anything, the sentence states that if there are $m$ such $S$-neighbours then $m (since there aren't $n$, and if there are $m>n$ then plainly there are $n$ (just take a subset of size $n$)). It doesn't state that any number of them *do* exist, though.2012-08-29

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