Theorem 4.14. A disjunctive GADL L is dually isomorphic to N0(L).
Proof. Let L be a disjunctive GADL. Define a mapping : L −→ N0(L) by
(x) = [x]∗, for all x ∈ L. Clearly, is well-defined. Let x, y ∈ L such that
(x) = (y). Then [x]∗ = [y]∗. Since L is disjunctive, we obtain that x = y.
Therefore is one to one. Let I ∈ N0(L). Then I = [x]∗, for some x ∈ L. Hence
(x) = [x]∗ = I. Therefore is onto.