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Now, addition of the equivalence classes is defined as follows.

For subset A and B of standard lattice L3, …

Note that, if g(A)Ug(B) = g(C), then [Cone A]R + [Cone B]R = [Cone C]R if and only if …


Shown on the left is addition of two classes [Cone A]R + [Cone E]R, where the blue closed trajectories below show the shape of In(A) and In(E).

Shown in the middle is addition of four classes [Cone A]R + [Cone B]R + [Cone C]R + [Cone D]R, where the blue trajectories below show the shape of In(A), In(B), In(C), and In(D).

And shown on the right is addition of two classes [Cone F]R + [Cone D]R, where the blue trajectories below show the shape of In(D) and In(F).

As you see, all of them are associated with the same standard roof and the same conjugate roof.
Thus, they belong to the same equivalent class. In other words, the equivalence class has three different algebraic expressions.