Proof Already Exists?

I believe the proof for the conjectured statement was proven in the affirmative in the paper "Fields of Surreal Numbers and Exponentiation" by Dries and Ehrlich. Specifically, Lemma 3.3 on page 6 :

If this satisfies the conjecture adequately great, if not, let me know if you would like to work toward a solution together on something similar or related.


-Vincent Russo


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