Coq Arithmetic Proof Completion FAQs

Question 1

What is the Coq Arithmetic Proof Completion skill?

Accepted Answer

It is a specialized capability for Claude Code designed to help developers complete formal proofs in Coq. It focuses specifically on natural number arithmetic, providing guidance on induction, lemma application, and goal simplification.

Question 2

How does this skill improve the formal verification workflow?

Accepted Answer

It streamlines the proof process by providing standardized patterns for induction, analyzing the proof state to suggest the next logical tactic, and offering debugging strategies for common pitfalls like incorrect induction variables or missing imports.

Question 3

Which specific Coq lemmas does this skill support?

Accepted Answer

The skill is optimized for standard library arithmetic lemmas, most notably 'plus_n_O' and 'plus_n_Sm'. it helps determine the correct rewrite direction and identifies when a property is definitional versus when it requires a lemma.

Question 4

When should I use this skill with Claude Code?

Accepted Answer

Use this skill when working on Coq source files (.v) that contain incomplete proofs (Admitted) or when you encounter difficulties with inductive steps involving properties like addition commutativity or associativity.

Question 5

Can Claude help debug failing Coq proofs using this skill?

Accepted Answer

Yes. The skill includes diagnostic features to identify why a proof is stuck, such as checking goal states with 'Show', verifying lemma signatures, and isolating problematic tactics to ensure the proof script compiles successfully.

Coq Arithmetic Proof Completion

Coq Arithmetic Proof Completion

Key Features

Use Cases

Key Features

Use Cases