prove-plus-comm
Guidance for proving mathematical properties in Coq using induction, specifically addition commutativity and similar arithmetic lemmas. This skill should be used when working with Coq proof assistants to complete induction proofs, fill in proof cases, or apply standard library lemmas like plus_n_O and plus_n_Sm.
npx skills add majiayu000/claude-skill-registry --skill prove-plus-comm --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# Proving Addition Commutativity in Coq ## Overview This skill provides guidance for completing induction proofs in Coq, particularly proofs involving arithmetic properties like addition commutativity (`n + m = m + n`). It covers the workflow for understanding incomplete proofs, identifying required lemmas, and verifying correctness through compilation. ## Workflow for Completing Coq Proofs ### Step 1: Understand the Proof Structure Before making any edits, read and understand the existing proof file: 1. Identify the theorem statement and what needs to be proved 2. Locate incomplete cases marked with `admit`, `Admitted`, or placeholder tactics 3. Understand the induction structure (base case vs inductive case) 4. Note which libraries are imported (e.g., `Require Import Arith`) ### Step 2: Analyze Each Case For induction proofs on natural numbers: **Base Case (n = 0):** - After `simpl`, determine what the goal simplifies to - Common pattern: proving `m = m + 0` requires the `plus_n_O` lemma - The `plus_n_O` lemma states: `forall n, n = n + 0` **Inductive Case (n = S n'):** - Identify the inductive hypothesis (IH) available in context - After `simpl`, the goal typically involves `S (
- Overview
- Workflow for Completing Coq Proofs
- Step 1: Understand the Proof Structure
- Step 2: Analyze Each Case
- Step 3: Apply Tactics
- Step 4: Verify with Compilation
- Verification Strategies
- Incremental Verification
- Check Goal States
- Library Verification
- Common Pitfalls
- Direction of Rewriting
- Missing Library Imports
- Assuming Lemma Existence
What does the prove-plus-comm skill do?
Guidance for proving mathematical properties in Coq using induction, specifically addition commutativity and similar arithmetic lemmas. This skill should be used when working with Coq proof assistants to complete induction proofs, fill in proof cases, or apply standard library lemmas like plus_n_O and plus_n_Sm.
How do I install it?
Run `npx skills add majiayu000/claude-skill-registry --skill prove-plus-comm --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From majiayu000/claude-skill-registry, a repository with 534 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.