[wizzwizz4]

Actually, some proofs take longer for the computer to verify than for a human (even an unskilled typist) to type out. Several hours to evaluate a two-page document isn't unusual. (I prefer to write optimised proofs, but it can take me weeks to find the correct abstractions for that.)

[UltraSane]

Are you talking about Lean 4? Lean 4 is usually pretty fast at verifying proofs and most proofs are created in interactive mode so are checked as they are typed.

A "two-page document" (perhaps 200-300 lines of code) would typically check in a matter of seconds to, at most, a few minutes. If it took hours, it would mean the file contains a pathological case that a developer would be expected to identify and fix. It is absolutely not a normal or "not unusual" occurrence.

[wizzwizz4]

Steps to reproduce:

1. Load a complex data structure, e.g. from JSON. (I do not consider typing out the JSON to be part of the human's job.)

2. Process the data, using the magic of functional programming. (Performance? What's that? Performance is not a priority.)

3. Add some helpful lemmas.

4. Prove the data processing stage was correct… but proving this in general is haaaard, so just make automation that's capable of proving it for most cases… eventually.

5. Great! It takes 3 minutes to run on my tiny examples. Now run it on the real data.

And that's where hours come from!

[UltraSane]

This is NOT what Lean 4 is designed to do. You seem to be using Lean 4 for what TLA+ is much better suited for.

[wizzwizz4]

If it is not suitable for programming, then it should not be branded as a programming language. Heck, its homepage says:

> Lean's metaprogramming capabilities enable users to extend the language with domain-specific notations and new proof automation techniques.