Develop rewriting support for Iris entailments and step-indexed distances

Develop a rewriting technique for Iris-Lean that supports rewriting by single entailments and step-indexed distances at a level comparable to Iris-Rocq's generalized setoid rewriting.

Background

Iris-Lean replaces setoid equivalence with equality where possible, allowing Lean's standard rewriting tools to handle algebraic and logical equivalences directly. However, single entailments and step-indexed distance relations are not yet supported as rewriting principles. The authors identify the development of a technique comparable to Iris-Rocq's rewriting support as unresolved, noting that existing tactics such as Mathlib's grw and König's rw' tactic are promising but insufficient.

References

We also note that Iris-Lean does not yet support rewriting by single entailments $\vdash$ or the step-indexed distances $\nequivB{n}$. Mathlib's \lstinline|grw| and König's original \lstinline|rw'| tactic \citep{koenig22} show promise, but we have yet to identify a technique that is on par with Iris-\rocq{}.

— Iris in Lean  (2609.24252 - Medeiros et al., 21 Sep 2026) in Section 3.2, “Benefits and costs”