6. An application

6.1 Application. It is easy to show that the only subdirectly irreducible distributive lattice is 2. Consequences:

(i) Every distributive lattice is a subdirect product of copies of 2.

(ii) The variety of distributive lattices is the same as Var$($2$)$.

(iii) Every distributive lattice $L$ can be represented as a lattice of subsets of some set (perhaps not all subsets), with operations $\cup,\cap$.