Open Research Index

sneed-and-feed/lean-theorems-1

Sneed & Feed Formalization Team

Palomar Registrypalomar/PALOMAR-2026-08-26-000013Aug 26, 2026math.MGscore 0

A complete, machine-checked Lean 4 formalization of the Sylvester–Gallai theorem (J. J. Sylvester 1893, T. Gallai 1944, L. M. Kelly 1948; Freek Wiedijk #98). Proves that every finite non-collinear set of points in the real Euclidean plane contains an ordinary line passing through exactly two points of the set, formalized via Kelly's minimal point-line distance argument. To the maintainers' knowledge, the theorem was not found in an exact declaration name, docstring, and type signature search of the pinned Mathlib revision (Mathlib v4.34.0-rc1).

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