pigeonhole-argument

The pigeonhole principle proves existence by placing n+1 items into n categories, which guarantees a collision. This skill identifies your items and categories, then constructs a formal mapping to verify that at least two items must share a category.

Yes, this skill provides a Lean-friendly formalization path for pigeonhole arguments. It translates combinatorial counting and mapping strategies into machine-checked proof logic, ensuring your existence proof is verifiable in the Lean prover.

You can solve problems like finding duplicates in attribute sets, proving mutual relationships in groups, or establishing divisibility properties via modular reasoning. The approach adapts to various n and k settings where items exceed available categories.

The best way is to specify a clear mapping strategy from items to categories and apply combinatorial counting. This skill adapts to varying n and k settings by identifying items as pigeons and categories as holes to guarantee a collision.

No prior formalization experience is strictly required to generate the logical argument, but leveraging the Lean-based formalization path for machine-checked verification works best if you have basic familiarity with the Lean prover and combinatorial counting.