[trissim]

Yes, many proofs are rfl. That's because we're doing engineering formalization, not pure math. The work is in getting the definitions right. Once you've correctly modeled Rust's compilation phases, item sources, and erasure semantics, the theorem that "RuntimeItem has no source field, therefore query_source returns none" should be rfl. That's the point.

The hard part isn't the proof tactics. The hard part is:

- Correctly modeling Rust's macro expansion semantics from the language reference

- Defining the compilation phases and when information is erased

- Structuring the types so that the impossibility is structural (RuntimeItem literally doesn't have a source field) If the theorems required 500 lines of tactic proofs, that would mean our model was wrong or overcomplicated. When you nail the definitions, rfl is the proof.

Compare to software verification: when you prove a sorting algorithm correct, the hard work is the loop invariants and the model, not the final QED. Tedious proof steps usually indicate you're fighting your abstractions.

The real question isn't "are the proofs short?" It's "can you attack the definitions?" The model claims RuntimeItem erases source info at compile-to-runtime. Either produce Rust code where RuntimeItem retains its macro provenance at runtime, or accept the model is correct. The rfl follows from the model being right.

[BalinKing]

> Compare to software verification: when you prove a sorting algorithm correct, the hard work is the loop invariants and the model, not the final QED. Tedious proof steps usually indicate you're fighting your abstractions.

This is a false statement when working with an interactive theorem prover like Lean. Even trivial things require mountains of effort, and even blatantly obvious facts will at least require a case analysis or something. It's a massive usability barrier (and one that AI can hopefully help with).

[trissim]

This is addressed in the paper's Preemptive Rebuttals section (Concern 9: "The Proofs Are Trivial").

At 2k lines of lean, the criticism was "these proofs are trivial." At 9k lines of lean with 541 theorems, the criticism is... still "trivial"? At what point does the objection become "I didn't read it"?

The rfl proofs are scaffolding. The substantive proofs (rust_lacks_introspection, Inconsistency.lean, Coherence.lean) are hundreds of lines of actual reasoning. This is in the paper.