21. The verification that this structure is a distributive lattice with the required universal property is routine. 22. This provides an alternative definition of a Boolean algebra, namely as any complemented distributive lattice . 23. Let be a bounded distributive lattice , and let denote the topology on is generated by. 24. This condition is called "'distributivity "'and gives rise to distributive lattices . 25. The deduction theorem holds for all first-order theories with the usual non-distributive lattice . 26. However, in a ( bounded ) distributive lattice every element will have at most one complement. 27. Each pairwise Stone space is bi-homeomorphic to the bitopological dual of some bounded distributive lattice . 28. However, it is still possible that two such terms denote the same element of the distributive lattice . 29. In the case of distributive lattices such an " M " is always a prime ideal. 30. These are laws of Boolean algebra whence the underlying poset of a Boolean algebra forms a distributive lattice .
