Let Q be an orthoposet. Let X be the set of states of Q. Recall that we use P(X) for the set of subsets of X, made into a preorder using subset. That is, the elements of P(X) are sets of states of Q, and we say that A < B in P(X) if A ⊆ B. Consider the function f : Q → P(X) given by
f(x) = {all states S of Q such that x ∈ S}
Notice that the line above says "not e". Prove that f is antitone.