i = isLowerSemimodular P
Let $r$ be the ranking of $P$. Then $P$ is lower semimodular if for every pair of vertices $a$ and $b$, $r(a) + r(b) \leq r(join(a,b)) + r(meet(a,b,))$.
The $n$ chain and the $n$ booleanLattice are lower semimodular.
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The following lattice is not lower semimodular.
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This method was ported from John Stembridge's Maple package available at http://www.math.lsa.umich.edu/~jrs/maple.html#posets.
The object isLowerSemimodular is a method function.