?. If, F ) is meet-irreducible then ? x (F ) is its unique cover. This implies that every ? x -closed set that contains ? x (F ), contains also ? x (F )

. To-sum-up, F ) is the only cover of ? x (F ) in F x \ ? ? * (x) and ? x (F ) is a subset of ? x (? x (F ) ? ? * (x)). We conclude that ? x (F ) is the only cover of ? x (F ) in F x

F. Fc and =. , Figure 7.4.2 depicts the correspondence between meet irreducible sets of F c and F cd . Then, table in figure 7.4.3 distinguishes closed sets in M 6 using the property 6. In this case M 6 = {{c}}. Then, we use property 7 to verify that ? d ({c}) is meet-irreducible in F cd : since ?({c} ? {d}) = {a, b, c, d} is equal to ?({b, c} ? {d}) = {a, b, c, d} where {b, c} is {c}'s cover that

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