[Lean Squad] feat(ci): Task 9 — fix elan SHA256, cache ordering, conditional lake update, proof summary

[Evangelink]

Improvements to lean-proofs.yml:

1. Fix SHA256 verification bug: the previous workflow hardcoded the SHA256
   hash from elan v3.1.0 but was downloading v4.2.1. The verification step
   would always fail once .lean files are committed. Now the SHA256 checksum
   file is downloaded from the same GitHub release and used for verification,
   so upgrading elan requires only a version bump.

2. Cache-before-install ordering: move the cache restore step to before the
   elan install step. Both elan install and lake update are now gated on
   cache-hit != 'true', so cold builds install/resolve while warm builds skip
   straight to lake build.

3. Conditional lake update: previously lake update ran unconditionally on
   every CI run, potentially drifting the pinned lake-manifest.json. Now it
   only runs on cache miss (i.e. the first run per toolchain/lakefile hash).

4. Proof summary step: after a successful build, post a markdown summary to
   the GitHub Actions step summary showing theorem/lemma count and the number
   of lines using sorry (stub markers).

🔬 Lean Squad — automated formal verification agent
Run: https://github.com/microsoft/testfx/actions/runs/25043800787

Co-authored-by: Copilot 223556219+Copilot@users.noreply.github.com

Fixes #7902

[Copilot]

Pull request overview

Updates the Lean proofs CI workflow to make elan installation/checksum verification more reliable, improve cache effectiveness, reduce unnecessary dependency resolution, and add a post-build proof metric summary.

Changes:

• Restore the elan/Lake cache earlier and gate elan install + lake update on cache misses.
• Fix elan SHA256 verification by downloading the checksum file from the same GitHub release as the archive.
• Add a GitHub Actions step summary with theorem/lemma counts and sorry usage counts.

Show a summary per file

File	Description
.github/workflows/lean-proofs.yml	Reorders caching/installation, updates checksum verification, conditions lake update, and adds a proof summary step.

Copilot's findings

• Files reviewed: 1/1 changed files
• Comments generated: 2

[Evangelink]

@copilot address review comments

[Copilot]

@copilot address review comments

Addressed in b4a6ebb:

1. Fixed SORRY_COUNT grep: replaced \bsorry\b with the POSIX portable word-boundary syntax \<sorry\> which works correctly in GNU grep without requiring -P.
2. Removed lake-manifest.json from the hashFiles() cache key expression — the file doesn't exist in the repo, so including it was misleading. The key now hashes only lean-toolchain and lakefile.toml.