counting-argument

Prove combinatorial identities using double counting or bijection techniques.

3|Updated Feb 9, 2026

Search Tags:#combinatorics #proof #inclusion-exclusion #counting #double-counting #bijection #lean-prover

Ready to run

npx skills add https://github.com/0bserver07/bourbaki --skill counting-argument

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: counting-argument
Source: https://github.com/0bserver07/bourbaki/tree/main/src/skills/counting-argument
Command: npx skills add https://github.com/0bserver07/bourbaki --skill counting-argument

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

Prove results by counting objects in clever ways.

Core Features & Use Cases

Technique A: Double Counting
Technique B: Bijection
Tools to use: symbolic_compute, sequence_lookup, lean_prover

Quick Start

Explain and build a counting argument to prove a combinatorial identity using double counting or bijection.

Frequently Asked Questions about counting-argument

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

FAQPage Schema

How do I prove combinatorial identities using double counting?▼

A bijection proves combinatorial identities by establishing a one-to-one correspondence between two sets, showing they have the same cardinality. This Skill uses bijection techniques to derive and verify equalities in discrete mathematics and combinatorics.

Can I use the lean prover to formalize counting arguments?▼

Yes, the lean prover is used to formalize and verify proofs derived from counting arguments. This Skill integrates lean prover alongside symbolic computation to ensure combinatorial proofs are rigorously validated.

What is the inclusion-exclusion principle in combinatorics?▼

The inclusion-exclusion principle is a counting technique used to calculate the cardinality of a union of sets. This Skill applies inclusion-exclusion alongside double counting and bijection to prove results in discrete mathematics.

Does this approach work for graph theory and combinatorics proofs?▼

Yes, counting arguments apply to both graph theory and combinatorics proofs. The Skill uses symbolic computation and sequence lookup to derive results where multiple counting methods prove equality in these discrete mathematics domains.

What's the best way to verify a combinatorial proof symbolically?▼

The best way to verify a combinatorial proof symbolically is using symbolic computation tools alongside sequence lookup. This Skill combines these tools with the lean prover to derive, cross-check, and formally verify combinatorial identities.