According to the definition we saw in theory, in any lattice, a modular pair is a pair $(a, b)$ of elements such that for all $x$ satisfying $$ a \land b \leq x \leq b, $$ we have $$ (x \lor a) \land b = x $$
Can you help me prove that in $S_7$, if $(a, b)$ is modular pair, then $(b, a)$ is modular pair?
Thanks
