https://github.com/mdbrnowski/lean-doodles
Doodles in Lean.
https://github.com/mdbrnowski/lean-doodles
formal-verification interactive-theorem-proving lean4
Last synced: about 1 month ago
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Doodles in Lean.
- Host: GitHub
- URL: https://github.com/mdbrnowski/lean-doodles
- Owner: mdbrnowski
- License: apache-2.0
- Created: 2025-06-30T20:10:02.000Z (about 1 year ago)
- Default Branch: main
- Last Pushed: 2026-05-28T15:39:08.000Z (2 months ago)
- Last Synced: 2026-06-05T00:13:31.237Z (about 2 months ago)
- Topics: formal-verification, interactive-theorem-proving, lean4
- Language: Lean
- Homepage:
- Size: 33.2 KB
- Stars: 1
- Watchers: 0
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Lean Doodles
Casual notes in [Lean](https://lean-lang.org): proofs of various theorems not tied to any specific project.
## Finite Integral Domain
[`FiniteIntegralDomain.lean`](/LeanDoodles/FiniteIntegralDomain.lean)
Every finite integral domain is a field.
## May's Theorem
[`MaysTheorem.lean`](/LeanDoodles/MaysTheorem.lean)
May's theorem states that majority rule is the only reasonable (near decisive, anonymous, neutral, and monotone) voting system for two candidates.
You can learn more about it on [my blog](https://dobranow.ski/posts/mays-theorem) or [Wikipedia](https://en.wikipedia.org/wiki/May%27s_theorem).
## Number Pairs
[`NumberPairs.lean`](/LeanDoodles/NumberPairs.lean)
A *Number Pair* for a given $d \in \mathbb{N}$ is a pair of numbers $(a, b)$ such that $b - a = d$ and the sum of the digits of $a$ is equal to the sum of the digits of $b$.
This module contains a constructive proof that a Number Pair exists if and only if $d$ is divisible by $9$.
Inspired by the Wincent DragonByte 2025, [problem N](https://www.wincentdragonbyte.com/static/qual2025/N_statement.html) from the qualification round.