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coq-proof-assistant

Develop interactive proofs and formalize mathematical theories in Coq.

17|2|Updated Feb 16, 2026
Search Tags:#formal verification#theorem proving#mathematical formalization#dependent types#proof assistant#coq
One-click install
npx skills add https://github.com/rainoftime/pl-skills --skill coq-proof-assistant
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: coq-proof-assistant
Source: https://github.com/rainoftime/pl-skills/tree/main/coq-proof-assistant
Command: npx skills add https://github.com/rainoftime/pl-skills --skill coq-proof-assistant

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill includes references (resource) and scripts (resource) components.

What problem does it solve?

This Skill assists in the rigorous process of formal verification and mathematical formalization, ensuring the correctness and reliability of software and mathematical theories.

Core Features & Use Cases

  • Proof Development: Write and manage interactive proofs for complex theorems.
  • Formalization: Structure mathematical theories and definitions within the Coq framework.
  • Verified Compilation: Assist in proving the correctness of compiler transformations.
  • Use Case: You need to formally prove that a sorting algorithm implemented in Coq is correct and always terminates.

Quick Start

Use the coq-proof-assistant skill to write a proof for the theorem forall n : nat, n + 0 = n.

Frequently Asked Questions about coq-proof-assistant

High-intent search queries and answers about installing and using this skill.

FAQPage Schema
How do I write a Coq proof for a theorem like forall n : nat, n + 0 = n?▼

To write a Coq proof for `forall n : nat, n + 0 = n`, you structure interactive proof scripts using tactics for induction and rewriting to verify the logical statement. This process ensures mathematical formalization correctness.

What is formal verification and how does a proof assistant handle mathematical formalization?▼

Formal verification uses proof assistants to rigorously check the correctness of software and mathematical theories. Mathematical formalization structures definitions and theorems within frameworks like Coq to guarantee logical reliability and verified compilation.

Can I use this approach to prove that a sorting algorithm implemented in Coq is correct and terminates?▼

Yes, you can prove a Coq sorting algorithm is correct and terminates by developing interactive proofs that verify program correctness. This involves structuring theories and handling induction to validate complex logical statements.

Does formal verification with dependent types work for proving compiler transformations?▼

Yes, formal verification with dependent types works for proving compiler transformations by assisting in verified compilation. You structure mathematical theories to prove the correctness of compiler transformations within the Coq proof assistant.

What is the best way to structure mathematical theories when handling induction in Coq?▼

The best way to structure mathematical theories in Coq is to define concepts rigorously and apply interactive proof development. Handling induction requires structuring definitions and theorems to effectively manage complex logical statements.

When do I need a proof assistant for verified software development instead of standard testing?▼

You need a proof assistant for verified software development when standard testing is insufficient to guarantee program correctness. Formal verification rigorously proves complex logical statements, ensuring mathematical formalization and software reliability.

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