double_counting

Community

Prove equalities by counting in two ways.

Authorbneb
Version1.0.0
Installs0

System Documentation

What problem does it solve?

Double counting (also: counting in two ways, Fubini for finite sets) establishes an algebraic identity by considering a bipartite relationship R ⊆ A × B. Counting the total number of "incidences" |R| by summing over the A-side gives one expression; summing over the B-side gives another. Equating them yields the identity.

Core Features & Use Cases

  • Formalizes proofs by counting incidences in bipartite relations to derive equalities.
  • Proves classic lemmas like the handshaking lemma, Vandermonde convolution, and binomial identities.
  • Educational: useful for teaching combinatorics and for constructing Lean-based proofs.

Quick Start

Provide a double-counting proof of a chosen identity by counting incidences in a finite bipartite relation.

Dependency Matrix

Required Modules

None required

Components

Standard package

💻 Claude Code Installation

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Please help me install this Skill:
Name: double_counting
Download link: https://github.com/bneb/perqed/archive/main.zip#double-counting

Please download this .zip file, extract it, and install it in the .claude/skills/ directory.
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