We prove that the lattice reduct of every lattice-ordered pregroup is semidistributive. This is a consequence of a certain weak form of the distributive law which holds in lattice-ordered pregroups.
Galatos, N., Jipsen, P., Kinyon, M., Přenosil, A.: Lattice-ordered pregroups are semi-distributive. Algebra Univers. 82, 16 (2021). https://doi.org/10.1007/s00012-020-00703-4