One doesn't need to be an expert in machine readable mathematics, to understand how to formalize it to a machine readable form.
If one takes the time to read the free book accompanying the metamath software, and re implements it in about a weekend time, you learn to understand how it works internally. Then playing around a little with mmj2 or so you quickly learn how to formalize a proof you understand. If you understand your own proof its easy to formalize it. One doesn't need to be "an expert in machine readable mathematics".
Do you have the weekend free? Perhaps you can take this new proof and show us how it is done.