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that for all x and y in the order, if x < y then ?(x) < ?(y), and
* The rank is consistent with the covering relation of the ordering, meaning that for all x and y, if y covers x then ?(y) = ?(x) + 1.The value of the rank function for an element of the poset is called its rank. Sometimes a graded poset is called a ranked poset but that phrase has other meanings; see Ranked poset. A rank or rank level of a graded poset is the subset of all the elements of the poset that have a given rank value.

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