I'm reading Stanley's Enumerative Combinatorics, and he says every lattice with at most six elements is modular. But what about the lattice below on the right? If $x,y$ are the two elements at the penultimate level, it seems $x\vee y :> x,y$ but $x \wedge y \not<: x,y$. What am I missing?
Edit: Never mind, he said every semimodular lattice with $\leq 6$ elements is modular.