OpenMath Rocq Theorem

Instructions

Set up the Rocq proving environment, validate opam switches, and prove downloaded OpenMath theorems. Assumes the theorem workspace was already created by the openmath-open-theorem skill.

This skill package is self-contained: it consists of this SKILL.md plus the local references/ files in this directory. It does not bundle or install sibling rocq-* companion skills.

Workflow checklist

• - [ ] Environment: Verify rocq (or coqc), dune, and opam are installed and the active opam switch matches the project's .opam-switch or opam file. See the rocq-setup skill for installation and switch management.
• [ ] Companion skills: If companion Rocq skills such as rocq-proof, rocq-ssreflect, rocq-setup, or rocq-dune are already installed in the active agent, use them. See references/companions.md for when each one is useful. This isolated package does not include their code and does not install them for you.
• [ ] Preflight: Confirm the environment is healthy before proving:

CODEBLOCK0

• - [ ] Prove: Follow the minimal Rocq proving loop in references/proof_playbook.md. If rocq-proof or rocq-ssreflect is already installed, use them as companion guidance; otherwise continue with the local workflow in this skill.
• [ ] Verify: Confirm dune build (or rocq compile <file>.v) passes and no admit or Admitted. remains:

CODEBLOCK1

• - [ ] Submit: Use the openmath-submit-theorem skill to hash and submit the proof.

Scripts

Action	Command	Use when
Check Rocq version	INLINECODE22	Verify the active opam switch has the expected Rocq release.
Verify stdlib loads

rocq -e 'From Stdlib Require Import Arith. Check Nat.add_comm.' | Confirm the standard library is reachable before proving. | | Build project | dune build | After each proof attempt; must exit 0 with no errors. | | Compile single file | rocq compile <file>.v | Quick check on a single .v file without a full dune build. | | Check for admits | grep -rn 'admit\|Admitted\.' *.v | Before submitting; must return no matches. | | Install opam deps | opam install . --deps-only | After cloning or changing the project opam file. |

Notes

• - Rocq version: OpenMath Rocq workspaces target Rocq 9.1.0 (current stable, September 2025) with Platform 2025.08.2.
• Companion skills: rocq-proof (proving methodology, tactic reference, Ltac2), rocq-ssreflect (SSReflect / MathComp style), rocq-setup (opam, toolchain, editor), and rocq-dune (build system, _CoqProject, dune stanzas) are useful companions when already installed. Optional companions: rocq-mwe, rocq-bisect, rocq-extraction, rocq-mathcomp-build.
• Install boundary: This isolated skill should not instruct copying unseen rocq-* directories into ~/.agents/skills or any other global skills directory. If you are installing from the full repository, review the companion skill folders there and copy them only into a deliberate project-local skills directory such as .codex/skills or .claude/skills.
• Stdlib prefix: Use From Stdlib Require Import for Rocq 9.x. The legacy From Coq Require Import still works with a deprecation warning; prefer From Stdlib for all new proofs.
• Verification status: A proof is complete only when dune build exits 0, no admit or Admitted. remains, and the LSP panel shows no errors or warnings.

References

Load when needed (one level from this file):

• - references/companions.md — When to use optional Rocq companion skills if they are already installed.
• references/languages.md — Rocq version, Stdlib prefix, libraries, and proof style.
• references/proof_playbook.md — Minimal standalone proving loop for downloaded OpenMath Rocq theorem workspaces.