# Show that the poset of partitions of [n] ordered by refinement is semimodular [on hold]

A poset is semimodular if it has the property that deg(x)+deg(y)≤deg(x∨y)+deg(x∧y)deg(x) + deg(y) \leq deg(x\vee y) + deg(x \wedge y) . Also, deg(x) for an x in the poset of partitions is the number of parts in the partition.

=================

=================