{"id":"palomar/PALOMAR-2026-08-31-000006","url":"https://github.com/sneed-and-feed/lean-theorems-1/tree/9630b06a3ba5bfd9eef5ff7140b2399f26fad899","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-08-31-000006-v1.json","repo":"https://github.com/sneed-and-feed/lean-theorems-1","tags":["math.MG","math.CO","msc:52A35","msc:52A20","msc:05D15","convex-geometry","combinatorics","lean-formalization"],"score":0,"title":"sneed-and-feed/lean-theorems-1","trust":"high","domain":"math.MG","source":"palomar","authors":["Sneed & Feed Formalization Team"],"reviews":0,"subject":"math.MG","summary":"A complete machine-checked Lean 4 formalization of Lovász's Colorful Helly Theorem (1974 / Bárány 1982). Proves that for any d + 1 finite families of convex sets in R^d such that every colorful transversal has a non-empty intersection, at least one entire family has a non-empty intersection. 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).","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-08-31","reactions":{},"formalized":true,"formalizes":[{"title":"A generalization of Carathéodory's theorem","identifier":"","relationship":"adapts"}]}