# Obtaining certain minimal elements for lattices

Let $L$ be a finite lattice and $L^{op}$ the opposite lattice. We can then look at the product lattice $U=L^{op} \times L$ and inside $U$ the poset $S_L=$ { $ (r_1,r_2 ) \in L^{op} \times L | r_2 \nleq r_1 $ }. My question is whether there is an easy way to obtain the poset $S_L$ for a given lattice $L$ together with the minimal elements $min(S_L)$ of $S_L$.