A proof using the FKG inequalities of the following result is obtained. LetPbe a partially ordered set ona1⩽a2⩽ ⋯ ⩽amandb1⩽b2⩽ ⋯ ⩽bn. LetP(x) be the proportion of linear extentions ofPfor whichxholds. Ifxandyare disjunctions of conjunctions of additional inequalities of the formai⩾bj, thenP(xandy) ⩾P(x)P(y). An example is provided that shows the result can be false if we don't assume the {ai} and {bj} are l
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