Existence Property Implies Disjunction Property
To prove the numerical existence property implies the disjunction property is trivial since a disjunction can be written as an existential formula,
- .
Therefore, assuming the numerical existence property, if is a theorem of, so is, by the numerical existence property there exists some such that is a theorem. Since is a numerial, we can check the value of, if then is a theorem and if then is a theorem, and the disjunction property is satisfied.
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