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applied: Rocq and Lean re-proofs of APP-1 to APP-4 (WO 4.2, 3 of 3) - #84
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The third of three pull requests for WO 4.2 (owner rulings 2026-11-12). Each leg restates the Agda definitions of verification/proofs/agda/Applied/ clause for clause and re-proves every theorem, the laws of the integer instance included. - verification/proofs/coq/Cohort.v: Rocq 8.18.0; the gate finds all 82 theorems closed under the global context. The standard library's PeanoNat and Lia prove the natural-number arithmetic; `Unset Lia Cache` keeps lia from writing a file. - verification/proofs/lean4/Cohort.lean: Lean 4.29.0, core only; the gate finds no axiom in any of the 95 theorems. No simp, omega or ac_rfl, which bring propext in; overlapping patterns are listed case by case for the same reason, and natLt and monus recurse on their second argument as Agda's do. - PROOF-STATUS records the legs and how the statements were compared; PROOF-NEEDS, EXPLAINME (15 proven of 17 legs), README, ROADMAP and the applied documents follow; the deed lists the two new files. No receipt records APP-1 to APP-4 yet, so no grade is derived for them. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_0136P7Zo9dheFQzYYWV49hAk
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hyperpolymath
marked this pull request as ready for review
November 12, 2026 03:38
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Summary
This is the third and last pull request for WO 4.2. It re-proves APP-1 to APP-4 in Rocq and Lean, as PROOF-POLICY §1 requires for theory. Each leg also re-proves the laws of the integer instance.
Each leg restates the Agda definitions of
verification/proofs/agda/Applied/clause for clause and proves every theorem again. Neither leg is a translation. With this PR, WO 4.2 is done.Changes
verification/proofs/coq/Cohort.v: the Rocq leg (Rocq 8.18.0). The gate'sPrint Assumptionsfinds all 82 theorems closed under the global context. The standard library'sPeanoNatandLiaprove the natural-number arithmetic.Unset Lia Cachekeepsliafrom writing a cache file beside the source.verification/proofs/lean4/Cohort.lean: the Lean leg (Lean 4.29.0, core only). The gate's audit finds no axiom in any of the 95 theorems. The Lean gate rejectspropext, which shaped this leg:simp,omegaorac_rfl, because each of them bringspropextin;propext, someet,zipWith,kandanddenominatorlist their cases without overlap; each is the same function;Intlemmas usepropext, so the leg uses Agda's integer type, with the same operations.natLtandmonuscopy Agda.Builtin.Nat's_<_and_-_, recursing on the second argument as Agda's do, so that the same terms reduce.docs/status/PROOF-STATUS.adoc: a record of APP-1 to APP-4. It holds the two legs and the statement comparison (§2.2): by reading, item by item, with every encoding difference listed. It notes that no receipt yet records these legs.PROOF-NEEDS: all four are proved in all three provers.:addedlist gains the two files, and the Rocq and Lean manifests list them as gated.RSR Quality Checklist
Required
As Applicable
docs/status/ROADMAP.adocupdatedTesting
I ran these in this session on
main3d24e93plus this change:just check-proofs: the Agda, Rocq and Lean gates all reportRESULT: PASS.bash tests/proofs/gate_controls_test.sh coqandlean4: in each, the clean control passes and the planted escape fails.bash tests/golden/check_controls_test.sh: all three controls fail as they should.just check-viewspasses, and so dovalidate-claude-md,validate-coapt,validate-state,validate-rsrandvalidate-repo-map.Next
Receipts for APP-1 to APP-4 need a CI run on the merged commit. Until those exist, no grade is derived for these obligations.
Screenshots
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