Determining reconstructability of erased proof terms under proof irrelevance

Determine whether there exist Lean proof terms such that, after erasing all proof terms to a constant symbol during e-graph encoding to overapproximate proof irrelevance, the erased proof terms cannot be completely reconstructed during subsequent proof generation in Lean.

Background

To align e-graph rewriting with Lean’s definitional equality, the authors overapproximate proof irrelevance by erasing all proof terms to a constant symbol during encoding. This simplifies equality saturation but necessitates reconstructing the erased proofs when producing Lean-checked certificates.

The authors express uncertainty about whether some erased proofs might be unrecoverable during reconstruction, which would impact the sound automation of proofs relying on proof irrelevance.