It looks like we have a "servant of every lover of" link between i and j if and only if …
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It looks like we have a "servant of every lover of" link between <math>i\!</math> and <math>j\!</math> if and only if <math>i \cdot S \supseteq L \cdot j.</math> It looks like the vacuous inclusions will make this rather non-intuitive.