While I was reading the book Surreal Numbers, by Donald E. Knuth I started to use coq to formally prove what the main characters were proving colloquially.

This is what gpt4 understood about surreal_numbers.v:

Me: Can you read the content of the surreal_numbers.v and let me know what is about ?

GPT-4: The file "surreal_numbers.v" appears to be a source code file written for use with the Coq proof assistant, a tool used in formal verification to ensure the correctness of mathematical proofs and software algorithms. The content includes imports of various modules required for working with lists, arithmetic, and logical propositions, suggesting that it deals with mathematical concepts or proofs.

The beginning of the file mentions "The Rock" and references J. H. W. H. Conway, likely referring to John Horton Conway, a British mathematician who invented surreal numbers. Surreal numbers are a mathematical concept that includes and extends the real numbers, allowing for the construction of numbers in terms of games. The text suggests that this file may include definitions, theorems, or proofs related to surreal numbers, possibly attempting to formalize their properties within the Coq system.

Given the specific mention of Conway and the context of surreal numbers, it's likely that this file is part of a mathematical exploration or formalization of surreal numbers using Coq. This would involve defining surreal numbers in a rigorous way and possibly proving properties about them within the Coq environment