double_counting
CommunityProve 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 requiredComponents
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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