proofs(lean4): close ET-2 — L1 conversion is decidable - #24
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Completes the MECH-1 milestone that Conversion.lean recorded as open.
Purely additive: four new modules under Systemet/L1/, plus append-only
entries in Systemet.lean, MANIFEST and Audit.lean. Syntax/Normal/Hsub/
Conversion.lean are untouched.
Landed (all statements verbatim from the ET-2 ledger entry):
SubstLemmas.lean substitution/weakening exchange family, incl.
nf_substTy — normalization commutes with hereditary
substitution (the beta case's whole content)
Soundness.lean soundness : DefEq t (embNf (nf t))
Completeness.lean completeness : DefEq t u -> nf t = nf u
defEq_iff_nf : DefEq t u <-> nf t = nf u
Decidable.lean decEqNf / decEqSp (hand-rolled mutual DecidableEq --
`deriving` does not work across the Nf/Sp pair)
decDefEq : (t u : Ty G k) -> Decidable (DefEq t u)
Method: exchange coordinates (swp/remSwap) with an Eq.rec cast toolkit
whose push lemmas are all `by subst h; rfl`, so definitional proof
irrelevance makes diagonal casts vanish. The subst/subst exchange needs a
SUM measure (kindSize k + kindSize b, tag, size) because the miss-then-hit
case folds appSp at the second kind.
Evidence (measured, not asserted):
clean rebuild from scratch Build completed successfully (16 jobs)
scripts/check-proofs.sh PASS, 20/20 headline items in trusted base
scripts/scan-dangerous.sh PASS
scripts/check-proof-status PASS after the doc update below
#print axioms on soundness, completeness, defEq_iff_nf, decDefEq,
decEqNf, decEqSp, nf_substTy -> [propext, Quot.sound] only; no
sorryAx, no user axioms, no Classical.choice.
Scope, stated honestly: DefEq here is beta + equivalence + congruence.
eta is NOT included and remains an OPEN row, so ET-3 is unaffected --
its eta and model directions stay open. PROOF-STATUS.adoc moves ET-2 to
proven *for the L1 core calculus* under the file's existing core-vs-full-
theory caveat, and the now-satisfied "ET-2 (finish)" OPEN row is removed.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Promotes the **ET-2 closure** (decidability of L1 conversion) onto `main`. ## Why this PR exists ET-2 was proven and merged in **PR #24** — but into `proofs/lean4-l1-l2`, **not `main`**. PR #17 had squash-merged that branch to `main` *before* ET-2 existed, so `main` holds the L1/L2 mechanization content while the ET-2 work sits only on the branch. No second PR to `main` was ever opened. Measured before this PR: `main...proofs/lean4-l1-l2` was **diverged, 4 ahead / 14 behind**, and all four ET-2 proof files returned **404 on `main`**. Anything reading `main` today correctly concludes ET-2 is still open. ## What lands on `main` | File | Contents | |---|---| | `Systemet/L1/SubstLemmas.lean` | substitution/weakening exchange family, incl. `nf_substTy` — normalization commutes with hereditary substitution (the whole content of the β case) | | `Systemet/L1/Soundness.lean` | `soundness : DefEq t (embNf (nf t))` | | `Systemet/L1/Completeness.lean` | `completeness : DefEq t u → nf t = nf u`; `defEq_iff_nf : DefEq t u ↔ nf t = nf u` | | `Systemet/L1/Decidable.lean` | `decEqNf` / `decEqSp` (hand-rolled mutual `DecidableEq` — `deriving` does not work across the `Nf`/`Sp` pair); `decDefEq : (t u : Ty Γ k) → Decidable (DefEq t u)` | Plus the `PROOF-STATUS.adoc` truth pass (`gated` 11 → 15, ET-2 row proven, MECH-1 row landed, the satisfied `ET-2 (finish)` OPEN row removed) and append-only `MANIFEST` / `Systemet.lean` / `Audit.lean` entries. ## Conflict resolution — read this bit The pre-PR sync merge (`0104c9c`) hit five conflicts. **Four were `add/add` artefacts of the squash in #17**, which makes git treat both sides as independent additions. None were resolved by a blanket `--ours`/`--theirs`: - `MANIFEST`, `Systemet.lean`, `Audit.lean` — verified `main`'s content is **byte-identical** to the branch's and the branch is a **strict superset** (adds exactly the four ET-2 entries). Branch side taken. - `PROOF-STATUS.adoc` — every difference is this branch's ET-2 update; `main` carried no independent edits. Branch side taken. - **`.github/workflows/proofs.yml` — a genuine two-sided merge.** The sides differed in *opposite* directions: `main` had the newer `actions/checkout@3d3c42e` (v7.0.1, from dependabot #26) while the branch had `curl --proto '=https' --tlsv1.2` (the Sonar S6506 fix). Took main's newer pin **and** re-applied the branch's https hardening, so neither is regressed. Both confirmed present post-resolution. ## Evidence (measured on the merged tree, not inherited from #24) - Cold rebuild after `rm -rf .lake/build` → **Build completed successfully (16 jobs)** - `scripts/check-proofs.sh lean4` → **PASS** (real exit 0); audit reports **20/20 headline items within the trusted base** - `scripts/scan-dangerous.sh` → **PASS** (real exit 0) - `scripts/check-proof-status.sh` → **PASS** (real exit 0) — 15 gated, document agrees - Forbidden-token scan on the four new proof files → clean - `#print axioms` on `soundness`, `completeness`, `defEq_iff_nf`, `decDefEq`, `decEqNf`, `decEqSp`, `nf_substTy` → **`[propext, Quot.sound]` only**; no `sorryAx`, no user axioms, not even `Classical.choice` Real exit codes were checked directly — piping a gate through `tail` and reading `$?` reports *tail's* status, which is how a red gate can look green. ## Scope — what this does *not* claim `DefEq` here is **β + equivalence + congruence. η is not included** and remains an OPEN row. **ET-3 is unaffected** — its η and model directions stay open. `PROOF-STATUS.adoc` marks ET-2 proven *for the L1 core calculus*, under the core-vs-full-theory caveat that file already carries. **ET-14 (TEA erasure) is untouched and remains the headline open problem**, gated on the owner's ET-16 / L0-lowering ADR. ## Merge notes Per the base ruleset, **squash is the only merge that works** here (rebase merges cannot be signed by GitHub bots), and the phantom required `Dependabot` context means this will need `--admin`. Not merged by me — that call is yours. 🤖 Generated with [Claude Code](https://claude.com/claude-code)
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Closes obligation ET-2 (decidability of L1 conversion) for the mechanized core calculus. This was the upstream blocker sitting under ET-14 / Phase 6.
Stacking and provenance
proofs/lean4-l1-l2, notmain. That branch is pushed but has no PR of its own; this stacks on it so the mechanization lands as one reviewable lineage. Retarget tomainifproofs/lean4-l1-l2merges first.lake buildas the judge). Two attempts reached full closure; this is the stronger one (38 theorems, faithful Keller–Altenkirch decomposition). Attempt artefacts were written to a scratch directory and applied here by hand — the campaign's own verify and adversarial-review stages were cut short by a monthly spend limit, so every check below was re-run manually rather than taken on an agent's word.What landed
Purely additive —
Syntax/Normal/Hsub/Conversion.leanare byte-identical; the only edits to existing files are append-only registry entries (18 insertions, 0 deletions).Systemet/L1/SubstLemmas.leannf_substTy— normalization commutes with hereditary substitution (the whole content of the beta case)Systemet/L1/Soundness.leansoundness : DefEq t (embNf (nf t))Systemet/L1/Completeness.leancompleteness : DefEq t u → nf t = nf u;defEq_iff_nf : DefEq t u ↔ nf t = nf uSystemet/L1/Decidable.leandecEqNf/decEqSp(hand-rolled mutualDecidableEq—derivingdoes not work across theNf/Sppair);decDefEq : (t u : Ty Γ k) → Decidable (DefEq t u)File layout matches the slots the ET-2 ledger entry already named.
Evidence (measured)
rm -rf .lake/build: Build completed successfully (16 jobs)scripts/check-proofs.sh lean4— PASS, audit reports 20/20 headline items within the trusted basescripts/scan-dangerous.sh— PASSscripts/check-proof-status.sh— PASS (exit 0) after thePROOF-STATUS.adocupdate#print axiomsonsoundness,completeness,defEq_iff_nf,decDefEq,decEqNf,decEqSp,nf_substTy→[propext, Quot.sound]only. NosorryAx, no user axioms, and not evenClassical.choice.DefEq/nf: none — the new theorems quantify over the originals fromConversion.lean, with generalΓandkand no added hypotheses.Scope — what this does not claim
DefEqhere is β + equivalence + congruence. η is not included, and remains an OPEN row. ET-3 is unaffected — its η and model directions stay open.PROOF-STATUS.adocmarks ET-2 proven for the L1 core calculus, under the caveat that file already carries about core-vs-full-theory claims, and drops the now-satisfied "ET-2 (finish)" OPEN row.ET-14 (TEA erasure) is untouched and remains the headline open problem. The campaign's TEA design track produced nothing — all three panelists and the judge died on the spend limit — so the ET-16 / L0 lowering ADR is still owner-gated and unstarted.
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