The statement written in Lean, is not actually a correct description of the Navier-Stokes problem. It's some other easier statement. That's why the Lean code may not be a proof.

Here's a quote from the paper.

"3.1. When the NL paper declares stronger statements than what Lean proves

We commence with an example that complements those in §2. In the following example the AI autoformalisation results in a different Lean proof of a weaker statement."

"Tracing the proof of (3.3) we find that the series arises from applying the Lean theorem coefficient_seminorm_bound, just as Figure 3 mentions. Consequently, the Lean results discussed in this section are weaker than (3.1) in the NL proof."

So the question is, was the Navier-Stokes problem framed properly in the lean code, or is some easier problem represented in the Lean code?

Here is their remark.

"Remark 3.4 (Further potential mistranslations of the Navier-Stokes proof). The above examples require careful manual checking of both the NL proof as well as the Lean proof, which is delicate and highly time consuming. Moreover, the fact that we display only two examples does not mean that these are the only cases of mistranslations."