Let a, b and c∈L be discussed in the following two cases:

(1) if a≤b and a≤c, then a∨b= b, a∨c = c, (a∨b)∧(a∨c )= b∧c,

On the other hand, from a≤b and a≤c to a≤b∧c, a∨(b∧c)= b∧c, so there is

(a∨b)∧(a∨c )= a∨(b∧c)

(2) If b≤a or c≤a, then a∨b= a or a∨c =a, so we can get (a∨b)∧(a∨c )= a from the law of absorption.

On the other hand, from b≤a or c≤a, b∧c ≤a, that is, a∨(b∧c)= a, so there are also.

(a∨b)∧(a∨c )= a∨(b∧c)

The law of distribution holds, so