overbar is:
# (Concatenation commutes, associates)
# (2 is a complemented lattice, with an upper bound of 1)
# (0 is the lower bound).
# (2 is a distributive lattice)

Where concatenation = OR, 1 = true, and 0 = false, or concatenation = AND, 1 = false, and 0 = true. (overbar is negation in both cases.)

If 0=1, (1)-(3)