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pick-any x ref xTo evaluate this proof in a given assumption base, we generate a fresh variable, say v85, and evaluate the body ref x with every free occurrence of x replaced by v85. Hence, in this case we will evaluate ref v85. According to the semantics of ref, the rule application ref v85 will yield the conclusion v85 = v85. Having finished evaluating the (renamed) body, the semantics of pick-any tell us that we can now produce the universal quantification (forall v85 (v85 = v85)) as the final conclusion of the entire pick-any. To make the result more readable, NDL will display this conclusion as (forall x (x = x)) instead of (forall v85 (v85 = v85)). That is, it will alphabetically rename the result, replacing the fresh variable with the actual eigenvariable that was used (in this case x). This is sound because recall that NDL treats alphabetically equivalent formulas as identical, so that